{"id":5364,"date":"2025-05-13T05:53:07","date_gmt":"2025-05-13T05:53:07","guid":{"rendered":"https:\/\/sigfigcalculator.io\/?p=5364"},"modified":"2025-05-13T11:38:25","modified_gmt":"2025-05-13T11:38:25","slug":"how-many-sig-figs","status":"publish","type":"post","link":"https:\/\/sigfigcalculator.io\/it\/how-many-sig-figs\/","title":{"rendered":"When adding, how many sig figs?"},"content":{"rendered":"<div class=\"sig-fig-article\">\r\n  <!-- Introduction Section -->\r\n  <section class=\"intro-section\">\r\n    \r\n    <div class=\"intro-content\">\r\n      <div class=\"intro-text\">\r\n        When performing calculations in science, engineering, and mathematics, significant figures (sig figs) play a crucial role in expressing the precision of your results. However, the rules for handling significant figures differ depending on whether you're adding, subtracting, multiplying, or dividing. This article focuses specifically on the rules for addition and subtraction.\r\n      <\/div>\r\n      <div class=\"intro-text\">\r\n        Understanding when and how to apply significant figure rules in addition is essential for accurate scientific calculations. We'll explore the fundamental principles, walk through examples, and provide interactive tools to help you master this important concept.\r\n      <\/div>\r\n    <\/div>\r\n  <\/section>\r\n\r\n  <!-- Table of Contents -->\r\n  <section class=\"toc-section\">\r\n    <div class=\"toc-title\">Contents<\/div>\r\n    <div class=\"toc-container\">\r\n      <a href=\"#understanding\" class=\"toc-item\">Understanding Significant Figures<\/a>\r\n      <a href=\"#addition-rule\" class=\"toc-item\">The Rule for Addition and Subtraction<\/a>\r\n      <a href=\"#examples\" class=\"toc-item\">Examples of Addition with Sig Figs<\/a>\r\n      <a href=\"#common-mistakes\" class=\"toc-item\">Common Mistakes to Avoid<\/a>\r\n      <a href=\"#comparison\" class=\"toc-item\">Addition vs. Multiplication Rules<\/a>\r\n      <a href=\"#applications\" class=\"toc-item\">Real-World Applications<\/a>\r\n      <a href=\"#practice\" class=\"toc-item\">Interactive Practice<\/a>\r\n      <a href=\"#conclusion\" class=\"toc-item\">Conclusion<\/a>\r\n    <\/div>\r\n  <\/section>\r\n\r\n  <!-- Understanding Significant Figures Section -->\r\n  <section id=\"understanding\" class=\"understanding-section\">\r\n    <div class=\"section-title\">Understanding Significant Figures<\/div>\r\n    <div class=\"section-content\">\r\n      <div class=\"definition-text\">\r\n        Significant figures are the digits in a measurement that carry meaning and contribute to its precision. Before diving into addition rules, let's quickly review what makes a digit significant:\r\n      <\/div>\r\n      \r\n      <div class=\"rules-container\">\r\n        <div class=\"rule-card\">\r\n          <div class=\"rule-number\">1<\/div>\r\n          <div class=\"rule-content\">\r\n            <div class=\"rule-title\">Non-zero digits are always significant<\/div>\r\n            <div class=\"rule-example\">\r\n              <span class=\"example-value\">1234<\/span> has 4 significant figures\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"rule-card\">\r\n          <div class=\"rule-number\">2<\/div>\r\n          <div class=\"rule-content\">\r\n            <div class=\"rule-title\">Zeros between non-zero digits are always significant<\/div>\r\n            <div class=\"rule-example\">\r\n              <span class=\"example-value\">1002<\/span> has 4 significant figures\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"rule-card\">\r\n          <div class=\"rule-number\">3<\/div>\r\n          <div class=\"rule-content\">\r\n            <div class=\"rule-title\">Leading zeros are never significant<\/div>\r\n            <div class=\"rule-example\">\r\n              <span class=\"example-value\">0.00123<\/span> has 3 significant figures\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"rule-card\">\r\n          <div class=\"rule-number\">4<\/div>\r\n          <div class=\"rule-content\">\r\n            <div class=\"rule-title\">Trailing zeros in a number with a decimal point are significant<\/div>\r\n            <div class=\"rule-example\">\r\n              <span class=\"example-value\">12.300<\/span> has 5 significant figures\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n      \r\n      <div class=\"sig-fig-visualization\">\r\n        <div class=\"visualization-title\">Visualizing Significant Figures<\/div>\r\n        <div class=\"visualization-container\">\r\n          <div class=\"number-display\" id=\"number-display\">12.340<\/div>\r\n          <div class=\"digit-container\" id=\"digit-container\"><\/div>\r\n        <\/div>\r\n        <div class=\"visualization-controls\">\r\n          <input type=\"text\" id=\"visualization-input\" placeholder=\"Enter a number\" value=\"12.340\">\r\n          <button id=\"visualize-btn\">Visualize<\/button>\r\n        <\/div>\r\n      <\/div>\r\n    <\/div>\r\n  <\/section>\r\n\r\n  <!-- The Rule for Addition and Subtraction -->\r\n  <section id=\"addition-rule\" class=\"addition-rule-section\">\r\n    <div class=\"section-title\">The Rule for Addition and Subtraction<\/div>\r\n    <div class=\"section-content\">\r\n      <div class=\"rule-highlight\">\r\n        <div class=\"rule-highlight-title\">The Key Rule<\/div>\r\n        <div class=\"rule-highlight-content\">\r\n          When adding or subtracting numbers, the result should have the same number of <span class=\"emphasis\">decimal places<\/span> as the measurement with the <span class=\"emphasis\">fewest decimal places<\/span>.\r\n        <\/div>\r\n      <\/div>\r\n      \r\n      <div class=\"rule-explanation\">\r\n        <div class=\"explanation-title\">Why This Rule?<\/div>\r\n        <div class=\"explanation-content\">\r\n          <div class=\"explanation-text\">\r\n            This rule differs from multiplication and division because addition and subtraction combine measurements directly, rather than creating ratios or products. The precision of the result is limited by the least precise measurement.\r\n          <\/div>\r\n          <div class=\"explanation-text\">\r\n            Think of it this way: if one measurement is only precise to the tenths place (e.g., 10.1 cm), then adding a more precise measurement (e.g., 5.237 cm) cannot make the result more precise than the tenths place.\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n      \r\n      <div class=\"rule-illustration\">\r\n        <div class=\"illustration-title\">Illustrated Example<\/div>\r\n        <div class=\"illustration-content\">\r\n          <div class=\"illustration-step\">\r\n            <div class=\"step-number\">1<\/div>\r\n            <div class=\"step-content\">\r\n              <div class=\"step-text\">Identify the number of decimal places in each measurement<\/div>\r\n              <div class=\"step-example\">\r\n                <div class=\"example-line\">10.1 cm \u2192 <span class=\"highlight\">1 decimal place<\/span><\/div>\r\n                <div class=\"example-line\">5.237 cm \u2192 3 decimal places<\/div>\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n          <div class=\"illustration-step\">\r\n            <div class=\"step-number\">2<\/div>\r\n            <div class=\"step-content\">\r\n              <div class=\"step-text\">Perform the addition<\/div>\r\n              <div class=\"step-example\">\r\n                <div class=\"example-line\">10.1 + 5.237 = 15.337<\/div>\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n          <div class=\"illustration-step\">\r\n            <div class=\"step-number\">3<\/div>\r\n            <div class=\"step-content\">\r\n              <div class=\"step-text\">Round to the number of decimal places in the least precise measurement<\/div>\r\n              <div class=\"step-example\">\r\n                <div class=\"example-line\">15.337 \u2192 <span class=\"highlight\">15.3<\/span> (rounded to 1 decimal place)<\/div>\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n    <\/div>\r\n  <\/section>\r\n\r\n  <!-- Examples of Addition with Sig Figs -->\r\n  <section id=\"examples\" class=\"examples-section\">\r\n    <div class=\"section-title\">Examples of Addition with Sig Figs<\/div>\r\n    <div class=\"section-content\">\r\n      <div class=\"examples-intro\">\r\n        Let's walk through several examples to solidify your understanding of how to apply the significant figures rule in addition and subtraction.\r\n      <\/div>\r\n      \r\n      <div class=\"examples-container\">\r\n        <div class=\"example-card\">\r\n          <div class=\"example-title\">Example 1: Simple Addition<\/div>\r\n          <div class=\"example-content\">\r\n            <div class=\"example-problem\">\r\n              <span class=\"problem-text\">Calculate: 12.3 + 5.67<\/span>\r\n            <\/div>\r\n            <div class=\"example-solution\">\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 1:<\/span> Identify decimal places\r\n                <div class=\"step-detail\">12.3 has 1 decimal place<\/div>\r\n                <div class=\"step-detail\">5.67 has 2 decimal places<\/div>\r\n              <\/div>\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 2:<\/span> Add the numbers\r\n                <div class=\"step-detail\">12.3 + 5.67 = 17.97<\/div>\r\n              <\/div>\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 3:<\/span> Round to 1 decimal place (from 12.3)\r\n                <div class=\"step-detail\">17.97 \u2192 <span class=\"final-answer\">18.0<\/span><\/div>\r\n              <\/div>\r\n              <div class=\"solution-note\">\r\n                Note: We write 18.0 (not just 18) to show that we have precision to the tenths place.\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"example-card\">\r\n          <div class=\"example-title\">Example 2: Multiple Numbers<\/div>\r\n          <div class=\"example-content\">\r\n            <div class=\"example-problem\">\r\n              <span class=\"problem-text\">Calculate: 1.23 + 45.6 + 7.891<\/span>\r\n            <\/div>\r\n            <div class=\"example-solution\">\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 1:<\/span> Identify decimal places\r\n                <div class=\"step-detail\">1.23 has 2 decimal places<\/div>\r\n                <div class=\"step-detail\">45.6 has 1 decimal place<\/div>\r\n                <div class=\"step-detail\">7.891 has 3 decimal places<\/div>\r\n              <\/div>\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 2:<\/span> Add the numbers\r\n                <div class=\"step-detail\">1.23 + 45.6 + 7.891 = 54.721<\/div>\r\n              <\/div>\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 3:<\/span> Round to 1 decimal place (from 45.6)\r\n                <div class=\"step-detail\">54.721 \u2192 <span class=\"final-answer\">54.7<\/span><\/div>\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"example-card\">\r\n          <div class=\"example-title\">Example 3: Subtraction<\/div>\r\n          <div class=\"example-content\">\r\n            <div class=\"example-problem\">\r\n              <span class=\"problem-text\">Calculate: 100.5 - 32.467<\/span>\r\n            <\/div>\r\n            <div class=\"example-solution\">\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 1:<\/span> Identify decimal places\r\n                <div class=\"step-detail\">100.5 has 1 decimal place<\/div>\r\n                <div class=\"step-detail\">32.467 has 3 decimal places<\/div>\r\n              <\/div>\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 2:<\/span> Subtract the numbers\r\n                <div class=\"step-detail\">100.5 - 32.467 = 68.033<\/div>\r\n              <\/div>\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 3:<\/span> Round to 1 decimal place (from 100.5)\r\n                <div class=\"step-detail\">68.033 \u2192 <span class=\"final-answer\">68.0<\/span><\/div>\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"example-card\">\r\n          <div class=\"example-title\">Example 4: Whole Numbers<\/div>\r\n          <div class=\"example-content\">\r\n            <div class=\"example-problem\">\r\n              <span class=\"problem-text\">Calculate: 25 + 3.42<\/span>\r\n            <\/div>\r\n            <div class=\"example-solution\">\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 1:<\/span> Identify decimal places\r\n                <div class=\"step-detail\">25 has 0 decimal places<\/div>\r\n                <div class=\"step-detail\">3.42 has 2 decimal places<\/div>\r\n              <\/div>\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 2:<\/span> Add the numbers\r\n                <div class=\"step-detail\">25 + 3.42 = 28.42<\/div>\r\n              <\/div>\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-label\">Step 3:<\/span> Round to 0 decimal places (from 25)\r\n                <div class=\"step-detail\">28.42 \u2192 <span class=\"final-answer\">28<\/span><\/div>\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n      \r\n      <div class=\"interactive-example\">\r\n        <div class=\"interactive-title\">Try It Yourself<\/div>\r\n        <div class=\"interactive-content\">\r\n          <div class=\"interactive-inputs\">\r\n            <div class=\"input-group\">\r\n              <label for=\"number1\">Number 1:<\/label>\r\n              <input type=\"text\" id=\"number1\" placeholder=\"Enter a number\">\r\n            <\/div>\r\n            <div class=\"input-group\">\r\n              <select id=\"operation\">\r\n                <option value=\"add\">+<\/option>\r\n                <option value=\"subtract\">-<\/option>\r\n              <\/select>\r\n            <\/div>\r\n            <div class=\"input-group\">\r\n              <label for=\"number2\">Number 2:<\/label>\r\n              <input type=\"text\" id=\"number2\" placeholder=\"Enter a number\">\r\n            <\/div>\r\n          <\/div>\r\n          <button id=\"calculate-btn\" class=\"calculate-button\">Calculate<\/button>\r\n          <div class=\"interactive-results\">\r\n            <div class=\"result-row\">\r\n              <span class=\"result-label\">Raw Result:<\/span>\r\n              <span id=\"raw-result\" class=\"result-value\">-<\/span>\r\n            <\/div>\r\n            <div class=\"result-row\">\r\n              <span class=\"result-label\">With Correct Sig Figs:<\/span>\r\n              <span id=\"sig-fig-result\" class=\"result-value\">-<\/span>\r\n            <\/div>\r\n            <div class=\"result-explanation\" id=\"result-explanation\"><\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n    <\/div>\r\n  <\/section>\r\n\r\n  <!-- Common Mistakes to Avoid -->\r\n  <section id=\"common-mistakes\" class=\"mistakes-section\">\r\n    <div class=\"section-title\">Common Mistakes to Avoid<\/div>\r\n    <div class=\"section-content\">\r\n      <div class=\"mistakes-intro\">\r\n        When working with significant figures in addition and subtraction, several common errors can lead to incorrect results. Here are the most frequent mistakes to watch out for:\r\n      <\/div>\r\n      \r\n      <div class=\"mistakes-container\">\r\n        <div class=\"mistake-card\">\r\n          <div class=\"mistake-icon\">\u26a0\ufe0f<\/div>\r\n          <div class=\"mistake-content\">\r\n            <div class=\"mistake-title\">Confusing Decimal Places with Significant Figures<\/div>\r\n            <div class=\"mistake-text\">\r\n              The rule for addition and subtraction is based on <span class=\"emphasis\">decimal places<\/span>, not the number of significant figures. Don't count significant figures when determining how to round your addition result.\r\n            <\/div>\r\n            <div class=\"mistake-example\">\r\n              <div class=\"example-incorrect\">\r\n                <span class=\"incorrect-label\">Incorrect:<\/span> Rounding 45.68 + 3.1 = 48.78 to 3 significant figures (48.8)\r\n              <\/div>\r\n              <div class=\"example-correct\">\r\n                <span class=\"correct-label\">Correct:<\/span> Rounding to 1 decimal place (48.8) because 3.1 has 1 decimal place\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"mistake-card\">\r\n          <div class=\"mistake-icon\">\u26a0\ufe0f<\/div>\r\n          <div class=\"mistake-content\">\r\n            <div class=\"mistake-title\">Applying Multiplication Rules to Addition<\/div>\r\n            <div class=\"mistake-text\">\r\n              Addition\/subtraction and multiplication\/division follow different rules for significant figures. Don't apply the \"least number of significant figures\" rule to addition problems.\r\n            <\/div>\r\n            <div class=\"mistake-example\">\r\n              <div class=\"example-incorrect\">\r\n                <span class=\"incorrect-label\">Incorrect approach:<\/span> \"12.34 + 5.6 should have 2 significant figures because 5.6 has 2 significant figures.\"\r\n              <\/div>\r\n              <div class=\"example-correct\">\r\n                <span class=\"correct-label\">Correct approach:<\/span> \"12.34 + 5.6 should have 1 decimal place because 5.6 has 1 decimal place.\"\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"mistake-card\">\r\n          <div class=\"mistake-icon\">\u26a0\ufe0f<\/div>\r\n          <div class=\"mistake-content\">\r\n            <div class=\"mistake-title\">Forgetting to Consider Whole Numbers<\/div>\r\n            <div class=\"mistake-text\">\r\n              Whole numbers have zero decimal places. When adding or subtracting a whole number with a decimal number, the result should be rounded to a whole number.\r\n            <\/div>\r\n            <div class=\"mistake-example\">\r\n              <div class=\"example-incorrect\">\r\n                <span class=\"incorrect-label\">Incorrect:<\/span> 25 + 3.42 = 28.42\r\n              <\/div>\r\n              <div class=\"example-correct\">\r\n                <span class=\"correct-label\">Correct:<\/span> 25 + 3.42 = 28\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"mistake-card\">\r\n          <div class=\"mistake-icon\">\u26a0\ufe0f<\/div>\r\n          <div class=\"mistake-content\">\r\n            <div class=\"mistake-title\">Rounding Intermediate Steps<\/div>\r\n            <div class=\"mistake-text\">\r\n              When performing multiple additions or subtractions, don't round intermediate results. Only round the final answer.\r\n            <\/div>\r\n            <div class=\"mistake-example\">\r\n              <div class=\"example-incorrect\">\r\n                <span class=\"incorrect-label\">Incorrect:<\/span> (12.34 + 5.6 = 17.9) + 8.912 = 26.812 \u2192 26.8\r\n              <\/div>\r\n              <div class=\"example-correct\">\r\n                <span class=\"correct-label\">Correct:<\/span> 12.34 + 5.6 + 8.912 = 26.852 \u2192 26.9\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n      \r\n      <div class=\"quiz-container\">\r\n        <div class=\"quiz-title\">Test Your Understanding<\/div>\r\n        <div class=\"quiz-content\">\r\n          <div class=\"quiz-question\" id=\"quiz-question\">Which of the following is correctly rounded according to significant figure rules for addition?<\/div>\r\n          <div class=\"quiz-options\">\r\n            <button class=\"quiz-option\" data-correct=\"false\">12.37 + 5.8 = 18.17<\/button>\r\n            <button class=\"quiz-option\" data-correct=\"true\">12.37 + 5.8 = 18.2<\/button>\r\n            <button class=\"quiz-option\" data-correct=\"false\">12.37 + 5.8 = 18<\/button>\r\n            <button class=\"quiz-option\" data-correct=\"false\">12.37 + 5.8 = 18.17 (3 sig figs)<\/button>\r\n          <\/div>\r\n          <div class=\"quiz-feedback\" id=\"quiz-feedback\"><\/div>\r\n          <button class=\"quiz-next\" id=\"quiz-next\">Next Question<\/button>\r\n        <\/div>\r\n      <\/div>\r\n    <\/div>\r\n  <\/section>\r\n\r\n  <!-- Addition vs. Multiplication Rules -->\r\n  <section id=\"comparison\" class=\"comparison-section\">\r\n    <div class=\"section-title\">Addition vs. Multiplication Rules<\/div>\r\n    <div class=\"section-content\">\r\n      <div class=\"comparison-intro\">\r\n        The rules for handling significant figures differ fundamentally between addition\/subtraction and multiplication\/division. Understanding these differences is crucial for performing calculations correctly.\r\n      <\/div>\r\n      \r\n      <div class=\"comparison-table\">\r\n        <div class=\"table-header\">\r\n          <div class=\"table-cell\">Operation<\/div>\r\n          <div class=\"table-cell\">Rule<\/div>\r\n          <div class=\"table-cell\">Example<\/div>\r\n          <div class=\"table-cell\">Explanation<\/div>\r\n        <\/div>\r\n        <div class=\"table-row\">\r\n          <div class=\"table-cell\">Addition & Subtraction<\/div>\r\n          <div class=\"table-cell\">Result has the same number of <span class=\"emphasis\">decimal places<\/span> as the measurement with the fewest decimal places<\/div>\r\n          <div class=\"table-cell\">12.37 + 5.8 = 18.2<\/div>\r\n          <div class=\"table-cell\">5.8 has 1 decimal place, so the result is rounded to 1 decimal place<\/div>\r\n        <\/div>\r\n        <div class=\"table-row\">\r\n          <div class=\"table-cell\">Multiplication & Division<\/div>\r\n          <div class=\"table-cell\">Result has the same number of <span class=\"emphasis\">significant figures<\/span> as the measurement with the fewest significant figures<\/div>\r\n          <div class=\"table-cell\">12.37 \u00d7 5.8 = 72<\/div>\r\n          <div class=\"table-cell\">5.8 has 2 significant figures, so the result is rounded to 2 significant figures<\/div>\r\n        <\/div>\r\n      <\/div>\r\n      \r\n      <div class=\"comparison-explanation\">\r\n        <div class=\"explanation-title\">Why the Difference?<\/div>\r\n        <div class=\"explanation-content\">\r\n          <div class=\"explanation-text\">\r\n            <span class=\"emphasis\">Addition and subtraction<\/span> combine measurements directly. The uncertainty in the result is determined by the absolute uncertainty in the least precise measurement (which corresponds to its decimal places).\r\n          <\/div>\r\n          <div class=\"explanation-text\">\r\n            <span class=\"emphasis\">Multiplication and division<\/span> combine measurements as ratios or products. The uncertainty in the result is determined by the relative uncertainty in the least precise measurement (which corresponds to its significant figures).\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n      \r\n      <div class=\"comparison-visual\">\r\n        <div class=\"visual-title\">Visual Comparison<\/div>\r\n        <div class=\"visual-container\">\r\n          <div class=\"visual-card\">\r\n            <div class=\"visual-header\">Addition (12.37 + 5.8)<\/div>\r\n            <div class=\"visual-content\">\r\n              <div class=\"number-line\">\r\n                <div class=\"number-representation\">\r\n                  <div class=\"digit-box\">1<\/div>\r\n                  <div class=\"digit-box\">2<\/div>\r\n                  <div class=\"digit-box\">.<\/div>\r\n                  <div class=\"digit-box\">3<\/div>\r\n                  <div class=\"digit-box\">7<\/div>\r\n                <\/div>\r\n                <div class=\"decimal-places\">\r\n                  <span><\/span>\r\n                  <span><\/span>\r\n                  <span><\/span>\r\n                  <span>1st<\/span>\r\n                  <span>2nd<\/span>\r\n                <\/div>\r\n              <\/div>\r\n              <div class=\"operation-symbol\">+<\/div>\r\n              <div class=\"number-line\">\r\n                <div class=\"number-representation\">\r\n                  <div class=\"digit-box\">5<\/div>\r\n                  <div class=\"digit-box\">.<\/div>\r\n                  <div class=\"digit-box highlight-box\">8<\/div>\r\n                <\/div>\r\n                <div class=\"decimal-places\">\r\n                  <span><\/span>\r\n                  <span><\/span>\r\n                  <span class=\"highlight-text\">1st<\/span>\r\n                <\/div>\r\n              <\/div>\r\n              <div class=\"operation-symbol\">=<\/div>\r\n              <div class=\"number-line\">\r\n                <div class=\"number-representation\">\r\n                  <div class=\"digit-box\">1<\/div>\r\n                  <div class=\"digit-box\">8<\/div>\r\n                  <div class=\"digit-box\">.<\/div>\r\n                  <div class=\"digit-box highlight-box\">2<\/div>\r\n                <\/div>\r\n                <div class=\"decimal-places\">\r\n                  <span><\/span>\r\n                  <span><\/span>\r\n                  <span><\/span>\r\n                  <span class=\"highlight-text\">1st<\/span>\r\n                <\/div>\r\n              <\/div>\r\n            <\/div>\r\n            <div class=\"visual-caption\">\r\n              Result rounded to 1 decimal place (from 5.8)\r\n            <\/div>\r\n          <\/div>\r\n          \r\n          <div class=\"visual-card\">\r\n            <div class=\"visual-header\">Multiplication (12.37 \u00d7 5.8)<\/div>\r\n            <div class=\"visual-content\">\r\n              <div class=\"number-line\">\r\n                <div class=\"number-representation\">\r\n                  <div class=\"digit-box sig-fig\">1<\/div>\r\n                  <div class=\"digit-box sig-fig\">2<\/div>\r\n                  <div class=\"digit-box\">.<\/div>\r\n                  <div class=\"digit-box sig-fig\">3<\/div>\r\n                  <div class=\"digit-box sig-fig\">7<\/div>\r\n                <\/div>\r\n                <div class=\"sig-fig-count\">\r\n                  <span>4 significant figures<\/span>\r\n                <\/div>\r\n              <\/div>\r\n              <div class=\"operation-symbol\">\u00d7<\/div>\r\n              <div class=\"number-line\">\r\n                <div class=\"number-representation\">\r\n                  <div class=\"digit-box sig-fig\">5<\/div>\r\n                  <div class=\"digit-box\">.<\/div>\r\n                  <div class=\"digit-box sig-fig highlight-box\">8<\/div>\r\n                <\/div>\r\n                <div class=\"sig-fig-count\">\r\n                  <span class=\"highlight-text\">2 significant figures<\/span>\r\n                <\/div>\r\n              <\/div>\r\n              <div class=\"operation-symbol\">=<\/div>\r\n              <div class=\"number-line\">\r\n                <div class=\"number-representation\">\r\n                  <div class=\"digit-box sig-fig\">7<\/div>\r\n                  <div class=\"digit-box sig-fig highlight-box\">2<\/div>\r\n                <\/div>\r\n                <div class=\"sig-fig-count\">\r\n                  <span class=\"highlight-text\">2 significant figures<\/span>\r\n                <\/div>\r\n              <\/div>\r\n            <\/div>\r\n            <div class=\"visual-caption\">\r\n              Result rounded to 2 significant figures (from 5.8)\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n    <\/div>\r\n  <\/section>\r\n\r\n  <!-- Real-World Applications -->\r\n  <section id=\"applications\" class=\"applications-section\">\r\n    <div class=\"section-title\">Real-World Applications<\/div>\r\n    <div class=\"section-content\">\r\n      <div class=\"applications-intro\">\r\n        Understanding significant figures in addition isn't just an academic exercise\u2014it has important real-world applications across many fields. Here's how proper application of these rules matters in practice:\r\n      <\/div>\r\n      \r\n      <div class=\"applications-grid\">\r\n        <div class=\"application-card\">\r\n          <div class=\"application-icon\">\ud83e\uddea<\/div>\r\n          <div class=\"application-title\">Laboratory Science<\/div>\r\n          <div class=\"application-content\">\r\n            When combining measurements from different instruments with varying precision, scientists must apply significant figure rules correctly to avoid implying greater precision than actually exists.\r\n          <\/div>\r\n          <div class=\"application-example\">\r\n            <span class=\"example-label\">Example:<\/span> A chemist measuring the total mass of a solution by adding the masses of the solute (1.234 g) and solvent (25.6 g) would report 26.8 g, not 26.834 g.\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"application-card\">\r\n          <div class=\"application-icon\">\ud83c\udfd7\ufe0f<\/div>\r\n          <div class=\"application-title\">Engineering<\/div>\r\n          <div class=\"application-content\">\r\n            Engineers must account for the precision of measurements when calculating total dimensions, loads, or other additive properties in their designs.\r\n          <\/div>\r\n          <div class=\"application-example\">\r\n            <span class=\"example-label\">Example:<\/span> When calculating the total length of a multi-component structure, the precision is limited by the least precise component measurement.\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"application-card\">\r\n          <div class=\"application-icon\">\ud83d\udc8a<\/div>\r\n          <div class=\"application-title\">Pharmacy<\/div>\r\n          <div class=\"application-content\">\r\n            Pharmacists must be precise when calculating total dosages or combining ingredients, where the rules for significant figures ensure appropriate precision.\r\n          <\/div>\r\n          <div class=\"application-example\">\r\n            <span class=\"example-label\">Example:<\/span> When combining multiple ingredients measured with different precision, the final formulation's precision is limited by the least precise measurement.\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"application-card\">\r\n          <div class=\"application-icon\">\ud83c\udf21\ufe0f<\/div>\r\n          <div class=\"application-title\">Meteorology<\/div>\r\n          <div class=\"application-content\">\r\n            Weather scientists apply significant figure rules when calculating average temperatures, total rainfall, or other cumulative measurements.\r\n          <\/div>\r\n          <div class=\"application-example\">\r\n            <span class=\"example-label\">Example:<\/span> When calculating the total annual rainfall by adding monthly measurements with varying precision, the result should reflect the precision of the least precise measurement.\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n      \r\n      <div class=\"case-study\">\r\n        <div class=\"case-study-title\">Case Study: Laboratory Analysis<\/div>\r\n        <div class=\"case-study-content\">\r\n          <div class=\"case-study-scenario\">\r\n            A laboratory technician needs to determine the total mass of a chemical compound by adding the masses of its components, measured on different scales:\r\n            <ul class=\"case-study-list\">\r\n              <li>Component A: 12.567 g (measured on an analytical balance with 0.001 g precision)<\/li>\r\n              <li>Component B: 3.45 g (measured on a less precise balance with 0.01 g precision)<\/li>\r\n              <li>Component C: 0.8 g (measured on a rough scale with 0.1 g precision)<\/li>\r\n            <\/ul>\r\n          <\/div>\r\n          <div class=\"case-study-solution\">\r\n            <div class=\"solution-title\">Solution:<\/div>\r\n            <div class=\"solution-steps\">\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-number\">1<\/span>\r\n                <span class=\"step-content\">Identify the decimal places: Component A (3), Component B (2), Component C (1)<\/span>\r\n              <\/div>\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-number\">2<\/span>\r\n                <span class=\"step-content\">Add the masses: 12.567 + 3.45 + 0.8 = 16.817 g<\/span>\r\n              <\/div>\r\n              <div class=\"solution-step\">\r\n                <span class=\"step-number\">3<\/span>\r\n                <span class=\"step-content\">Round to 1 decimal place (from Component C): 16.8 g<\/span>\r\n              <\/div>\r\n            <\/div>\r\n            <div class=\"solution-explanation\">\r\n              Reporting the result as 16.817 g would incorrectly imply that all components were measured with 0.001 g precision, which is not the case. The correct result of 16.8 g honestly reflects the limitations of the least precise measurement.\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n    <\/div>\r\n  <\/section>\r\n\r\n  <!-- Interactive Practice -->\r\n  <section id=\"practice\" class=\"practice-section\">\r\n    <div class=\"section-title\">Interactive Practice<\/div>\r\n    <div class=\"section-content\">\r\n      <div class=\"practice-intro\">\r\n        The best way to master significant figures in addition is through practice. Try these interactive tools and problems to test your understanding.\r\n      <\/div>\r\n      \r\n      <div class=\"practice-tools\">\r\n        <div class=\"sig-fig-calculator\">\r\n          <div class=\"calculator-title\">Significant Figures Calculator<\/div>\r\n          <div class=\"calculator-description\">Enter multiple numbers to add or subtract with the correct significant figures:<\/div>\r\n          <div class=\"calculator-inputs\">\r\n            <div class=\"multi-input-container\" id=\"multi-input-container\">\r\n              <div class=\"input-row\">\r\n                <input type=\"text\" class=\"number-input\" placeholder=\"Enter a number\">\r\n                <select class=\"operation-select\">\r\n                  <option value=\"add\">+<\/option>\r\n                  <option value=\"subtract\">-<\/option>\r\n                <\/select>\r\n              <\/div>\r\n              <div class=\"input-row\">\r\n                <input type=\"text\" class=\"number-input\" placeholder=\"Enter a number\">\r\n                <button class=\"remove-btn\" style=\"visibility: hidden;\">\u00d7<\/button>\r\n              <\/div>\r\n            <\/div>\r\n            <button id=\"add-number-btn\" class=\"add-number-btn\">+ Add Number<\/button>\r\n          <\/div>\r\n          <button id=\"multi-calculate-btn\" class=\"calculate-button\">Calculate<\/button>\r\n          <div class=\"calculator-results\">\r\n            <div class=\"result-row\">\r\n              <span class=\"result-label\">Raw Result:<\/span>\r\n              <span id=\"multi-raw-result\" class=\"result-value\">-<\/span>\r\n            <\/div>\r\n            <div class=\"result-row\">\r\n              <span class=\"result-label\">With Correct Sig Figs:<\/span>\r\n              <span id=\"multi-sig-fig-result\" class=\"result-value\">-<\/span>\r\n            <\/div>\r\n            <div class=\"result-explanation\" id=\"multi-result-explanation\"><\/div>\r\n          <\/div>\r\n        <\/div>\r\n        \r\n        <div class=\"practice-problems\">\r\n          <div class=\"problems-title\">Practice Problems<\/div>\r\n          <div class=\"problems-container\">\r\n            <div class=\"problem-display\" id=\"problem-display\">\r\n              <div class=\"problem-number\">Problem 1 of 5<\/div>\r\n              <div class=\"problem-text\" id=\"problem-text\">Calculate 23.45 + 6.7 with the correct number of significant figures.<\/div>\r\n              <div class=\"problem-input-container\">\r\n                <input type=\"text\" id=\"problem-answer\" class=\"problem-input\" placeholder=\"Your answer\">\r\n                <button id=\"check-answer-btn\" class=\"check-button\">Check<\/button>\r\n              <\/div>\r\n              <div class=\"problem-feedback\" id=\"problem-feedback\"><\/div>\r\n              <button id=\"next-problem-btn\" class=\"next-button\">Next Problem<\/button>\r\n            <\/div>\r\n            <div class=\"progress-container\">\r\n              <div class=\"progress-bar\">\r\n                <div class=\"progress-fill\" id=\"progress-fill\" style=\"width: 20%;\"><\/div>\r\n              <\/div>\r\n              <div class=\"progress-stats\">\r\n                <span id=\"correct-count\">0<\/span> correct out of <span id=\"total-attempted\">0<\/span> attempted\r\n              <\/div>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n      \r\n      <div class=\"decimal-places-tool\">\r\n        <div class=\"tool-title\">Decimal Places Visualizer<\/div>\r\n        <div class=\"tool-description\">\r\n          This tool helps you visualize the decimal places in numbers to determine how to round your addition or subtraction results.\r\n        <\/div>\r\n        <div class=\"tool-content\">\r\n          <div class=\"tool-inputs\">\r\n            <div class=\"input-group\">\r\n              <label for=\"decimal-input\">Enter a number:<\/label>\r\n              <input type=\"text\" id=\"decimal-input\" placeholder=\"e.g., 123.456\">\r\n              <button id=\"visualize-decimal-btn\">Visualize<\/button>\r\n            <\/div>\r\n          <\/div>\r\n          <div class=\"visualization-result\" id=\"decimal-visualization\">\r\n            <div class=\"placeholder-text\">Enter a number to visualize its decimal places<\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n    <\/div>\r\n  <\/section>\r\n\r\n  <!-- Conclusion -->\r\n  <section id=\"conclusion\" class=\"conclusion-section\">\r\n    <div class=\"section-title\">Conclusion<\/div>\r\n    <div class=\"section-content\">\r\n      <div class=\"conclusion-text\">\r\n        Understanding how to handle significant figures in addition and subtraction is a fundamental skill in scientific and mathematical calculations. By following the key rule\u2014rounding to the same number of decimal places as the measurement with the fewest decimal places\u2014you ensure that your results accurately reflect the precision of your data.\r\n      <\/div>\r\n      \r\n      <div class=\"conclusion-text\">\r\n        Remember that this rule differs from multiplication and division, which focus on the number of significant figures rather than decimal places. This distinction is crucial for performing calculations correctly across different operations.\r\n      <\/div>\r\n      \r\n      <div class=\"key-takeaways\">\r\n        <div class=\"takeaways-title\">Key Takeaways<\/div>\r\n        <div class=\"takeaways-list\">\r\n          <div class=\"takeaway-item\">\r\n            <div class=\"takeaway-number\">1<\/div>\r\n            <div class=\"takeaway-content\">In addition and subtraction, round to the same number of decimal places as the measurement with the fewest decimal places.<\/div>\r\n          <\/div>\r\n          <div class=\"takeaway-item\">\r\n            <div class=\"takeaway-number\">2<\/div>\r\n            <div class=\"takeaway-content\">Don't confuse the rules for addition\/subtraction with those for multiplication\/division.<\/div>\r\n          <\/div>\r\n          <div class=\"takeaway-item\">\r\n            <div class=\"takeaway-number\">3<\/div>\r\n            <div class=\"takeaway-content\">Whole numbers have zero decimal places and limit the precision of your result accordingly.<\/div>\r\n          <\/div>\r\n          <div class=\"takeaway-item\">\r\n            <div class=\"takeaway-number\">4<\/div>\r\n            <div class=\"takeaway-content\">Only round your final answer, not intermediate steps in multi-step calculations.<\/div>\r\n          <\/div>\r\n          <div class=\"takeaway-item\">\r\n            <div class=\"takeaway-number\">5<\/div>\r\n            <div class=\"takeaway-content\">Proper application of significant figure rules ensures that your results honestly reflect the precision of your measurements.<\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/div>\r\n      \r\n      <div class=\"conclusion-text\">\r\n        With practice and attention to detail, applying significant figure rules in addition and subtraction will become second nature. This skill is invaluable across scientific disciplines, engineering, and any field where precise measurements and calculations are essential.\r\n      <\/div>\r\n    <\/div>\r\n  <\/section>\r\n\r\n<style>\r\n  \/* Base Styles *\/\r\n  .sig-fig-article {\r\n    font-family: 'Inter', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, sans-serif;\r\n    max-width: 1000px;\r\n    margin: 0 auto;\r\n    color: #333;\r\n    line-height: 1.6;\r\n    background-color: #fff;\r\n  }\r\n  \r\n  .sig-fig-article * {\r\n    box-sizing: border-box;\r\n  }\r\n  \r\n  \/* Section Styles *\/\r\n  .intro-section, .understanding-section, .addition-rule-section, .examples-section, \r\n  .mistakes-section, .comparison-section, .applications-section, .practice-section, \r\n  .conclusion-section, .toc-section {\r\n    margin-bottom: 3rem;\r\n    padding: 2rem;\r\n    border-radius: 8px;\r\n    background-color: #fff;\r\n    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);\r\n  }\r\n  \r\n  \/* Introduction Section *\/\r\n  .intro-section {\r\n    background: linear-gradient(135deg, #f8f9fa 0%, #e9ecef 100%);\r\n    text-align: center;\r\n    padding: 3rem 2rem;\r\n  }\r\n  \r\n  .article-title {\r\n    font-size: 2.5rem;\r\n    color: #2c3e50;\r\n    margin-bottom: 0.5rem;\r\n    font-weight: 700;\r\n    line-height: 1.2;\r\n  }\r\n  \r\n  .article-subtitle {\r\n    font-size: 1.2rem;\r\n    color: #6c757d;\r\n    margin-bottom: 2rem;\r\n  }\r\n  \r\n  .intro-content {\r\n    max-width: 800px;\r\n    margin: 0 auto;\r\n  }\r\n  \r\n  .intro-text {\r\n    font-size: 1.1rem;\r\n    margin-bottom: 1.5rem;\r\n    text-align: left;\r\n  }\r\n  \r\n  \/* Table of Contents *\/\r\n  .toc-section {\r\n    background-color: #f8f9fa;\r\n  }\r\n  \r\n  .toc-title {\r\n    font-size: 1.5rem;\r\n    font-weight: 600;\r\n    margin-bottom: 1rem;\r\n    color: #2c3e50;\r\n  }\r\n  \r\n  .toc-container {\r\n    display: flex;\r\n    flex-wrap: wrap;\r\n    gap: 0.5rem;\r\n  }\r\n  \r\n  .toc-item {\r\n    background-color: #fff;\r\n    padding: 0.75rem 1.25rem;\r\n    border-radius: 4px;\r\n    text-decoration: none;\r\n    color: #3498db;\r\n    font-weight: 500;\r\n    box-shadow: 0 2px 4px rgba(0, 0, 0, 0.05);\r\n    transition: all 0.2s ease;\r\n    flex: 1 1 200px;\r\n  }\r\n  \r\n  .toc-item:hover {\r\n    background-color: #3498db;\r\n    color: #fff;\r\n    transform: translateY(-2px);\r\n    box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);\r\n  }\r\n  \r\n  \/* Section Headers *\/\r\n  .section-title {\r\n    font-size: 1.8rem;\r\n    color: #2c3e50;\r\n    margin-bottom: 1.5rem;\r\n    font-weight: 600;\r\n    border-bottom: 2px solid #e9ecef;\r\n    padding-bottom: 0.75rem;\r\n  }\r\n  \r\n  .section-content {\r\n    font-size: 1rem;\r\n  }\r\n  \r\n  \/* Understanding Section *\/\r\n  .definition-text {\r\n    margin-bottom: 1.5rem;\r\n    font-size: 1.05rem;\r\n  }\r\n  \r\n  .rules-container {\r\n    display: grid;\r\n    grid-template-columns: repeat(auto-fill, minmax(300px, 1fr));\r\n    gap: 1.5rem;\r\n    margin-bottom: 2rem;\r\n  }\r\n  \r\n  .rule-card {\r\n    background-color: #fff;\r\n    border-radius: 8px;\r\n    padding: 1.5rem;\r\n    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);\r\n    display: flex;\r\n    align-items: flex-start;\r\n    transition: transform 0.3s ease, box-shadow 0.3s ease;\r\n  }\r\n  \r\n  .rule-card:hover {\r\n    transform: translateY(-5px);\r\n    box-shadow: 0 8px 16px rgba(0, 0, 0, 0.1);\r\n  }\r\n  \r\n  .rule-number {\r\n    background-color: #3498db;\r\n    color: white;\r\n    width: 40px;\r\n    height: 40px;\r\n    border-radius: 50%;\r\n    display: flex;\r\n    align-items: center;\r\n    justify-content: center;\r\n    font-weight: 600;\r\n    margin-right: 1rem;\r\n    flex-shrink: 0;\r\n  }\r\n  \r\n  .rule-content {\r\n    flex-grow: 1;\r\n  }\r\n  \r\n  .rule-title {\r\n    font-weight: 600;\r\n    color: #2c3e50;\r\n    margin-bottom: 0.75rem;\r\n    font-size: 1.05rem;\r\n  }\r\n  \r\n  .rule-example {\r\n    background-color: #f8f9fa;\r\n    padding: 0.75rem;\r\n    border-radius: 4px;\r\n    margin-top: 0.75rem;\r\n    font-size: 0.95rem;\r\n  }\r\n  \r\n  .example-value {\r\n    font-weight: 600;\r\n    color: #3498db;\r\n    font-family: 'Courier New', monospace;\r\n  }\r\n  \r\n  .sig-fig-visualization {\r\n    background-color: #f8f9fa;\r\n    padding: 1.5rem;\r\n    border-radius: 8px;\r\n    margin-top: 2rem;\r\n  }\r\n  \r\n  .visualization-title {\r\n    font-size: 1.2rem;\r\n    font-weight: 600;\r\n    color: #2c3e50;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .visualization-container {\r\n    background-color: #fff;\r\n    padding: 1.5rem;\r\n    border-radius: 8px;\r\n    box-shadow: 0 2px 8px rgba(0, 0, 0, 0.05);\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .number-display {\r\n    font-size: 2rem;\r\n    font-weight: 600;\r\n    color: #2c3e50;\r\n    text-align: center;\r\n    margin-bottom: 1rem;\r\n    font-family: 'Courier New', monospace;\r\n  }\r\n  \r\n  .digit-container {\r\n    display: flex;\r\n    justify-content: center;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .visualization-controls {\r\n    display: flex;\r\n    gap: 0.75rem;\r\n  }\r\n  \r\n  .visualization-controls input {\r\n    flex-grow: 1;\r\n    padding: 0.75rem;\r\n    border: 1px solid #ced4da;\r\n    border-radius: 4px;\r\n    font-size: 1rem;\r\n  }\r\n  \r\n  .visualization-controls button {\r\n    background-color: #3498db;\r\n    color: white;\r\n    border: none;\r\n    padding: 0.75rem 1.25rem;\r\n    border-radius: 4px;\r\n    font-size: 1rem;\r\n    font-weight: 500;\r\n    cursor: pointer;\r\n    transition: background-color 0.2s;\r\n  }\r\n  \r\n  .visualization-controls button:hover {\r\n    background-color: #2980b9;\r\n  }\r\n  \r\n  \/* Addition Rule Section *\/\r\n  .rule-highlight {\r\n    background-color: #e8f4f8;\r\n    border-left: 4px solid #3498db;\r\n    padding: 1.5rem;\r\n    margin-bottom: 1.5rem;\r\n    border-radius: 0 8px 8px 0;\r\n  }\r\n  \r\n  .rule-highlight-title {\r\n    font-weight: 600;\r\n    color: #3498db;\r\n    margin-bottom: 0.75rem;\r\n    font-size: 1.2rem;\r\n  }\r\n  \r\n  .rule-highlight-content {\r\n    font-size: 1.1rem;\r\n    line-height: 1.7;\r\n  }\r\n  \r\n  .emphasis {\r\n    font-weight: 600;\r\n    color: #3498db;\r\n    background-color: rgba(52, 152, 219, 0.1);\r\n    padding: 0.1rem 0.3rem;\r\n    border-radius: 3px;\r\n  }\r\n  \r\n  .rule-explanation {\r\n    margin-bottom: 2rem;\r\n  }\r\n  \r\n  .explanation-title {\r\n    font-weight: 600;\r\n    color: #2c3e50;\r\n    margin-bottom: 0.75rem;\r\n    font-size: 1.1rem;\r\n  }\r\n  \r\n  .explanation-text {\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .rule-illustration {\r\n    background-color: #f8f9fa;\r\n    padding: 1.5rem;\r\n    border-radius: 8px;\r\n  }\r\n  \r\n  .illustration-title {\r\n    font-weight: 600;\r\n    color: #2c3e50;\r\n    margin-bottom: 1rem;\r\n    font-size: 1.1rem;\r\n  }\r\n  \r\n  .illustration-step {\r\n    display: flex;\r\n    align-items: flex-start;\r\n    margin-bottom: 1.25rem;\r\n  }\r\n  \r\n  .illustration-step:last-child {\r\n    margin-bottom: 0;\r\n  }\r\n  \r\n  .step-number {\r\n    background-color: #3498db;\r\n    color: white;\r\n    width: 30px;\r\n    height: 30px;\r\n    border-radius: 50%;\r\n    display: flex;\r\n    align-items: center;\r\n    justify-content: center;\r\n    font-weight: 600;\r\n    margin-right: 1rem;\r\n    flex-shrink: 0;\r\n  }\r\n  \r\n  .step-content {\r\n    flex-grow: 1;\r\n  }\r\n  \r\n  .step-text {\r\n    margin-bottom: 0.5rem;\r\n  }\r\n  \r\n  .step-example {\r\n    background-color: #fff;\r\n    padding: 0.75rem;\r\n    border-radius: 4px;\r\n    font-family: 'Courier New', monospace;\r\n  }\r\n  \r\n  .example-line {\r\n    margin-bottom: 0.5rem;\r\n  }\r\n  \r\n  .example-line:last-child {\r\n    margin-bottom: 0;\r\n  }\r\n  \r\n  .highlight {\r\n    background-color: #fff3cd;\r\n    padding: 0.1rem 0.3rem;\r\n    border-radius: 3px;\r\n    font-weight: 500;\r\n    color: #856404;\r\n  }\r\n  \r\n  \/* Examples Section *\/\r\n  .examples-intro {\r\n    margin-bottom: 1.5rem;\r\n    font-size: 1.05rem;\r\n  }\r\n  \r\n  .examples-container {\r\n    display: grid;\r\n    grid-template-columns: repeat(auto-fill, minmax(400px, 1fr));\r\n    gap: 1.5rem;\r\n    margin-bottom: 2rem;\r\n  }\r\n  \r\n  .example-card {\r\n    background-color: #fff;\r\n    border-radius: 8px;\r\n    overflow: hidden;\r\n    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);\r\n  }\r\n  \r\n  .example-title {\r\n    background-color: #3498db;\r\n    color: white;\r\n    padding: 1rem 1.5rem;\r\n    font-weight: 600;\r\n    font-size: 1.1rem;\r\n  }\r\n  \r\n  .example-content {\r\n    padding: 1.5rem;\r\n  }\r\n  \r\n  .example-problem {\r\n    margin-bottom: 1rem;\r\n    font-size: 1.1rem;\r\n    font-weight: 500;\r\n  }\r\n  \r\n  .solution-step {\r\n    margin-bottom: 0.75rem;\r\n  }\r\n  \r\n  .solution-step:last-child {\r\n    margin-bottom: 0;\r\n  }\r\n  \r\n  .step-label {\r\n    font-weight: 600;\r\n    color: #3498db;\r\n    margin-right: 0.5rem;\r\n  }\r\n  \r\n  .step-detail {\r\n    margin-top: 0.25rem;\r\n    margin-left: 1rem;\r\n    font-family: 'Courier New', monospace;\r\n  }\r\n  \r\n  .final-answer {\r\n    font-weight: 600;\r\n    color: #28a745;\r\n    background-color: rgba(40, 167, 69, 0.1);\r\n    padding: 0.1rem 0.3rem;\r\n    border-radius: 3px;\r\n  }\r\n  \r\n  .solution-note {\r\n    margin-top: 1rem;\r\n    font-style: italic;\r\n    color: #6c757d;\r\n  }\r\n  \r\n  .interactive-example {\r\n    background-color: #f8f9fa;\r\n    padding: 1.5rem;\r\n    border-radius: 8px;\r\n    margin-top: 2rem;\r\n  }\r\n  \r\n  .interactive-title {\r\n    font-size: 1.2rem;\r\n    font-weight: 600;\r\n    color: #2c3e50;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .interactive-inputs {\r\n    display: flex;\r\n    flex-wrap: wrap;\r\n    gap: 0.75rem;\r\n    margin-bottom: 1.25rem;\r\n    align-items: flex-end;\r\n  }\r\n  \r\n  .input-group {\r\n    flex-grow: 1;\r\n    min-width: 150px;\r\n  }\r\n  \r\n  .input-group label {\r\n    display: block;\r\n    margin-bottom: 0.5rem;\r\n    font-weight: 500;\r\n    color: #495057;\r\n  }\r\n  \r\n  .input-group input, .input-group select {\r\n    width: 100%;\r\n    padding: 0.75rem;\r\n    border: 1px solid #ced4da;\r\n    border-radius: 4px;\r\n    font-size: 1rem;\r\n  }\r\n  \r\n  .calculate-button {\r\n    background-color: #3498db;\r\n    color: white;\r\n    border: none;\r\n    padding: 0.75rem 1.5rem;\r\n    border-radius: 4px;\r\n    font-size: 1rem;\r\n    font-weight: 500;\r\n    cursor: pointer;\r\n    transition: background-color 0.2s;\r\n  }\r\n  \r\n  .calculate-button:hover {\r\n    background-color: #2980b9;\r\n  }\r\n  \r\n  .interactive-results {\r\n    background-color: #fff;\r\n    padding: 1rem;\r\n    border-radius: 4px;\r\n    margin-top: 1.25rem;\r\n    border: 1px solid #e9ecef;\r\n  }\r\n  \r\n  .result-row {\r\n    display: flex;\r\n    justify-content: space-between;\r\n    margin-bottom: 0.75rem;\r\n  }\r\n  \r\n  .result-row:last-of-type {\r\n    margin-bottom: 0.5rem;\r\n  }\r\n  \r\n  .result-label {\r\n    font-weight: 500;\r\n    color: #495057;\r\n  }\r\n  \r\n  .result-value {\r\n    font-family: 'Courier New', monospace;\r\n    font-weight: 600;\r\n    color: #3498db;\r\n  }\r\n  \r\n  .result-explanation {\r\n    font-size: 0.9rem;\r\n    color: #6c757d;\r\n    margin-top: 0.5rem;\r\n    padding-top: 0.5rem;\r\n    border-top: 1px solid #e9ecef;\r\n  }\r\n  \r\n  \/* Mistakes Section *\/\r\n  .mistakes-intro {\r\n    margin-bottom: 1.5rem;\r\n    font-size: 1.05rem;\r\n  }\r\n  \r\n  .mistakes-container {\r\n    display: grid;\r\n    grid-template-columns: repeat(auto-fill, minmax(300px, 1fr));\r\n    gap: 1.5rem;\r\n    margin-bottom: 2rem;\r\n  }\r\n  \r\n  .mistake-card {\r\n    background-color: #fff4f4;\r\n    border-radius: 8px;\r\n    padding: 1.5rem;\r\n    display: flex;\r\n    align-items: flex-start;\r\n    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);\r\n  }\r\n  \r\n  .mistake-icon {\r\n    font-size: 1.5rem;\r\n    margin-right: 1rem;\r\n    color: #e74c3c;\r\n  }\r\n  \r\n  .mistake-title {\r\n    font-weight: 600;\r\n    color: #e74c3c;\r\n    margin-bottom: 0.75rem;\r\n    font-size: 1.05rem;\r\n  }\r\n  \r\n  .mistake-example {\r\n    background-color: #fff;\r\n    padding: 0.75rem;\r\n    border-radius: 4px;\r\n    margin-top: 0.75rem;\r\n    font-size: 0.95rem;\r\n  }\r\n  \r\n  .incorrect-label {\r\n    color: #e74c3c;\r\n    font-weight: 600;\r\n    margin-right: 0.5rem;\r\n  }\r\n  \r\n  .correct-label {\r\n    color: #28a745;\r\n    font-weight: 600;\r\n    margin-right: 0.5rem;\r\n  }\r\n  \r\n  .example-incorrect {\r\n    margin-bottom: 0.5rem;\r\n  }\r\n  \r\n  .quiz-container {\r\n    background-color: #f8f9fa;\r\n    padding: 1.5rem;\r\n    border-radius: 8px;\r\n    margin-top: 2rem;\r\n  }\r\n  \r\n  .quiz-title {\r\n    font-size: 1.2rem;\r\n    font-weight: 600;\r\n    color: #2c3e50;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .quiz-question {\r\n    font-size: 1.1rem;\r\n    margin-bottom: 1.25rem;\r\n  }\r\n  \r\n  .quiz-options {\r\n    display: grid;\r\n    grid-template-columns: repeat(auto-fill, minmax(200px, 1fr));\r\n    gap: 0.75rem;\r\n    margin-bottom: 1.25rem;\r\n  }\r\n  \r\n  .quiz-option {\r\n    background-color: white;\r\n    border: 1px solid #ced4da;\r\n    border-radius: 4px;\r\n    padding: 0.75rem;\r\n    font-size: 1rem;\r\n    cursor: pointer;\r\n    transition: all 0.2s;\r\n    text-align: left;\r\n  }\r\n  \r\n  .quiz-option:hover {\r\n    border-color: #3498db;\r\n    background-color: #f0f7fc;\r\n  }\r\n  \r\n  .quiz-feedback {\r\n    min-height: 24px;\r\n    font-weight: 500;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .quiz-next {\r\n    background-color: #3498db;\r\n    color: white;\r\n    border: none;\r\n    padding: 0.75rem 1.5rem;\r\n    border-radius: 4px;\r\n    font-size: 1rem;\r\n    font-weight: 500;\r\n    cursor: pointer;\r\n    transition: background-color 0.2s;\r\n    display: none;\r\n  }\r\n  \r\n  .quiz-next:hover {\r\n    background-color: #2980b9;\r\n  }\r\n  \r\n  \/* Comparison Section *\/\r\n  .comparison-intro {\r\n    margin-bottom: 1.5rem;\r\n    font-size: 1.05rem;\r\n  }\r\n  \r\n  .comparison-table {\r\n    background-color: #fff;\r\n    border-radius: 8px;\r\n    overflow: hidden;\r\n    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);\r\n    margin-bottom: 2rem;\r\n  }\r\n  \r\n  .table-header {\r\n    background-color: #3498db;\r\n    color: white;\r\n    display: grid;\r\n    grid-template-columns: 1fr 2fr 1fr 2fr;\r\n    font-weight: 600;\r\n  }\r\n  \r\n  .table-row {\r\n    display: grid;\r\n    grid-template-columns: 1fr 2fr 1fr 2fr;\r\n    border-bottom: 1px solid #e9ecef;\r\n  }\r\n  \r\n  .table-row:last-child {\r\n    border-bottom: none;\r\n  }\r\n  \r\n  .table-cell {\r\n    padding: 1rem;\r\n    display: flex;\r\n    align-items: center;\r\n  }\r\n  \r\n  .comparison-explanation {\r\n    margin-bottom: 2rem;\r\n  }\r\n  \r\n  .comparison-visual {\r\n    background-color: #f8f9fa;\r\n    padding: 1.5rem;\r\n    border-radius: 8px;\r\n  }\r\n  \r\n  .visual-container {\r\n    display: grid;\r\n    grid-template-columns: repeat(auto-fill, minmax(400px, 1fr));\r\n    gap: 1.5rem;\r\n    margin-top: 1rem;\r\n  }\r\n  \r\n  .visual-card {\r\n    background-color: #fff;\r\n    border-radius: 8px;\r\n    overflow: hidden;\r\n    box-shadow: 0 2px 8px rgba(0, 0, 0, 0.05);\r\n  }\r\n  \r\n  .visual-header {\r\n    background-color: #3498db;\r\n    color: white;\r\n    padding: 0.75rem 1rem;\r\n    font-weight: 600;\r\n  }\r\n  \r\n  .visual-content {\r\n    padding: 1.5rem;\r\n  }\r\n  \r\n  .visual-caption {\r\n    text-align: center;\r\n    padding: 0.75rem;\r\n    background-color: #f8f9fa;\r\n    color: #6c757d;\r\n    font-style: italic;\r\n  }\r\n  \r\n  .number-line {\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .number-representation {\r\n    display: flex;\r\n    justify-content: center;\r\n    margin-bottom: 0.5rem;\r\n  }\r\n  \r\n  .digit-box {\r\n    width: 40px;\r\n    height: 40px;\r\n    display: flex;\r\n    align-items: center;\r\n    justify-content: center;\r\n    border: 1px solid #ced4da;\r\n    margin: 0 2px;\r\n    font-family: 'Courier New', monospace;\r\n    font-weight: 600;\r\n    font-size: 1.2rem;\r\n  }\r\n  \r\n  .highlight-box {\r\n    background-color: #fff3cd;\r\n    border-color: #ffeeba;\r\n  }\r\n  \r\n  .decimal-places, .sig-fig-count {\r\n    display: flex;\r\n    justify-content: center;\r\n    font-size: 0.8rem;\r\n    color: #6c757d;\r\n  }\r\n  \r\n  .decimal-places span {\r\n    width: 40px;\r\n    margin: 0 2px;\r\n    text-align: center;\r\n  }\r\n  \r\n  .highlight-text {\r\n    color: #856404;\r\n    font-weight: 600;\r\n  }\r\n  \r\n  .operation-symbol {\r\n    text-align: center;\r\n    font-size: 1.5rem;\r\n    margin: 1rem 0;\r\n    color: #6c757d;\r\n  }\r\n  \r\n  .sig-fig {\r\n    background-color: #d4edda;\r\n    border-color: #c3e6cb;\r\n  }\r\n  \r\n  .sig-fig-count {\r\n    margin-top: 0.5rem;\r\n  }\r\n  \r\n  \/* Applications Section *\/\r\n  .applications-intro {\r\n    margin-bottom: 1.5rem;\r\n    font-size: 1.05rem;\r\n  }\r\n  \r\n  .applications-grid {\r\n    display: grid;\r\n    grid-template-columns: repeat(auto-fill, minmax(250px, 1fr));\r\n    gap: 1.5rem;\r\n    margin-bottom: 2rem;\r\n  }\r\n  \r\n  .application-card {\r\n    background-color: #fff;\r\n    border-radius: 8px;\r\n    padding: 1.5rem;\r\n    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);\r\n    transition: transform 0.3s ease, box-shadow 0.3s ease;\r\n  }\r\n  \r\n  .application-card:hover {\r\n    transform: translateY(-5px);\r\n    box-shadow: 0 8px 16px rgba(0, 0, 0, 0.1);\r\n  }\r\n  \r\n  .application-icon {\r\n    font-size: 2rem;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .application-title {\r\n    font-weight: 600;\r\n    color: #2c3e50;\r\n    margin-bottom: 0.75rem;\r\n    font-size: 1.1rem;\r\n  }\r\n  \r\n  .application-content {\r\n    margin-bottom: 1rem;\r\n    color: #495057;\r\n  }\r\n  \r\n  .application-example {\r\n    background-color: #f8f9fa;\r\n    padding: 0.75rem;\r\n    border-radius: 4px;\r\n    font-size: 0.9rem;\r\n  }\r\n  \r\n  .example-label {\r\n    font-weight: 600;\r\n    color: #6c757d;\r\n    margin-right: 0.25rem;\r\n  }\r\n  \r\n  .case-study {\r\n    background-color: #f8f9fa;\r\n    border-radius: 8px;\r\n    overflow: hidden;\r\n    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);\r\n    margin-top: 2rem;\r\n  }\r\n  \r\n  .case-study-title {\r\n    background-color: #3498db;\r\n    color: white;\r\n    padding: 1rem 1.5rem;\r\n    font-weight: 600;\r\n    font-size: 1.1rem;\r\n  }\r\n  \r\n  .case-study-content {\r\n    padding: 1.5rem;\r\n  }\r\n  \r\n  .case-study-scenario {\r\n    margin-bottom: 1.5rem;\r\n  }\r\n  \r\n  .case-study-list {\r\n    padding-left: 1.5rem;\r\n    margin: 1rem 0;\r\n  }\r\n  \r\n  .case-study-list li {\r\n    margin-bottom: 0.5rem;\r\n  }\r\n  \r\n  .solution-title {\r\n    font-weight: 600;\r\n    color: #2c3e50;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .solution-steps {\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .solution-explanation {\r\n    background-color: #e8f4f8;\r\n    padding: 1rem;\r\n    border-radius: 4px;\r\n    color: #2c3e50;\r\n    font-style: italic;\r\n  }\r\n  \r\n  \/* Practice Section *\/\r\n  .practice-intro {\r\n    margin-bottom: 1.5rem;\r\n    font-size: 1.05rem;\r\n  }\r\n  \r\n  .practice-tools {\r\n    display: grid;\r\n    grid-template-columns: repeat(auto-fill, minmax(400px, 1fr));\r\n    gap: 1.5rem;\r\n    margin-bottom: 2rem;\r\n  }\r\n  \r\n  .sig-fig-calculator, .practice-problems {\r\n    background-color: #fff;\r\n    border-radius: 8px;\r\n    overflow: hidden;\r\n    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);\r\n  }\r\n  \r\n  .calculator-title, .problems-title {\r\n    background-color: #3498db;\r\n    color: white;\r\n    padding: 1rem 1.5rem;\r\n    font-weight: 600;\r\n    font-size: 1.1rem;\r\n  }\r\n  \r\n  .calculator-description {\r\n    padding: 1rem 1.5rem;\r\n    color: #6c757d;\r\n  }\r\n  \r\n  .calculator-inputs {\r\n    padding: 0 1.5rem;\r\n  }\r\n  \r\n  .multi-input-container {\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .input-row {\r\n    display: flex;\r\n    gap: 0.5rem;\r\n    margin-bottom: 0.5rem;\r\n  }\r\n  \r\n  .number-input {\r\n    flex-grow: 1;\r\n    padding: 0.75rem;\r\n    border: 1px solid #ced4da;\r\n    border-radius: 4px;\r\n    font-size: 1rem;\r\n  }\r\n  \r\n  .operation-select {\r\n    width: 60px;\r\n    padding: 0.75rem 0.5rem;\r\n    border: 1px solid #ced4da;\r\n    border-radius: 4px;\r\n    font-size: 1rem;\r\n  }\r\n  \r\n  .remove-btn {\r\n    background-color: #e74c3c;\r\n    color: white;\r\n    border: none;\r\n    width: 30px;\r\n    height: 30px;\r\n    border-radius: 50%;\r\n    display: flex;\r\n    align-items: center;\r\n    justify-content: center;\r\n    cursor: pointer;\r\n    font-size: 1.2rem;\r\n    align-self: center;\r\n  }\r\n  \r\n  .add-number-btn {\r\n    background-color: #2ecc71;\r\n    color: white;\r\n    border: none;\r\n    padding: 0.5rem 1rem;\r\n    border-radius: 4px;\r\n    font-size: 0.9rem;\r\n    cursor: pointer;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .calculator-results {\r\n    padding: 1.5rem;\r\n    background-color: #f8f9fa;\r\n  }\r\n  \r\n  .problems-container {\r\n    padding: 1.5rem;\r\n  }\r\n  \r\n  .problem-display {\r\n    background-color: #f8f9fa;\r\n    padding: 1.5rem;\r\n    border-radius: 8px;\r\n    margin-bottom: 1.5rem;\r\n  }\r\n  \r\n  .problem-number {\r\n    font-weight: 600;\r\n    color: #6c757d;\r\n    margin-bottom: 0.75rem;\r\n  }\r\n  \r\n  .problem-text {\r\n    font-size: 1.1rem;\r\n    margin-bottom: 1.25rem;\r\n  }\r\n  \r\n  .problem-input-container {\r\n    display: flex;\r\n    gap: 0.75rem;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .problem-input {\r\n    flex-grow: 1;\r\n    padding: 0.75rem;\r\n    border: 1px solid #ced4da;\r\n    border-radius: 4px;\r\n    font-size: 1rem;\r\n  }\r\n  \r\n  .check-button {\r\n    background-color: #3498db;\r\n    color: white;\r\n    border: none;\r\n    padding: 0.75rem 1.25rem;\r\n    border-radius: 4px;\r\n    font-size: 1rem;\r\n    font-weight: 500;\r\n    cursor: pointer;\r\n  }\r\n  \r\n  .problem-feedback {\r\n    min-height: 24px;\r\n    font-weight: 500;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .next-button {\r\n    background-color: #2ecc71;\r\n    color: white;\r\n    border: none;\r\n    padding: 0.75rem 1.25rem;\r\n    border-radius: 4px;\r\n    font-size: 1rem;\r\n    font-weight: 500;\r\n    cursor: pointer;\r\n    width: 100%;\r\n    display: none;\r\n  }\r\n  \r\n  .progress-container {\r\n    margin-top: 1.5rem;\r\n  }\r\n  \r\n  .progress-bar {\r\n    height: 8px;\r\n    background-color: #e9ecef;\r\n    border-radius: 4px;\r\n    overflow: hidden;\r\n    margin-bottom: 0.5rem;\r\n  }\r\n  \r\n  .progress-fill {\r\n    height: 100%;\r\n    background-color: #3498db;\r\n    border-radius: 4px;\r\n    transition: width 0.3s ease;\r\n  }\r\n  \r\n  .progress-stats {\r\n    text-align: right;\r\n    font-size: 0.9rem;\r\n    color: #6c757d;\r\n  }\r\n  \r\n  .decimal-places-tool {\r\n    background-color: #fff;\r\n    border-radius: 8px;\r\n    overflow: hidden;\r\n    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);\r\n    margin-top: 2rem;\r\n  }\r\n  \r\n  .tool-title {\r\n    background-color: #3498db;\r\n    color: white;\r\n    padding: 1rem 1.5rem;\r\n    font-weight: 600;\r\n    font-size: 1.1rem;\r\n  }\r\n  \r\n  .tool-description {\r\n    padding: 1rem 1.5rem;\r\n    color: #6c757d;\r\n  }\r\n  \r\n  .tool-content {\r\n    padding: 1.5rem;\r\n  }\r\n  \r\n  .tool-inputs {\r\n    margin-bottom: 1.5rem;\r\n  }\r\n  \r\n  .visualization-result {\r\n    background-color: #f8f9fa;\r\n    padding: 1.5rem;\r\n    border-radius: 8px;\r\n    min-height: 100px;\r\n    display: flex;\r\n    align-items: center;\r\n    justify-content: center;\r\n  }\r\n  \r\n  .placeholder-text {\r\n    color: #6c757d;\r\n    font-style: italic;\r\n  }\r\n  \r\n  \/* Conclusion Section *\/\r\n  .conclusion-section {\r\n    background-color: #f8f9fa;\r\n  }\r\n  \r\n  .conclusion-text {\r\n    margin-bottom: 1.5rem;\r\n    font-size: 1.05rem;\r\n  }\r\n  \r\n  .key-takeaways {\r\n    background-color: #fff;\r\n    border-radius: 8px;\r\n    overflow: hidden;\r\n    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);\r\n    margin: 2rem 0;\r\n  }\r\n  \r\n  .takeaways-title {\r\n    background-color: #3498db;\r\n    color: white;\r\n    padding: 1rem 1.5rem;\r\n    font-weight: 600;\r\n    font-size: 1.1rem;\r\n  }\r\n  \r\n  .takeaways-list {\r\n    padding: 1.5rem;\r\n  }\r\n  \r\n  .takeaway-item {\r\n    display: flex;\r\n    align-items: flex-start;\r\n    margin-bottom: 1rem;\r\n  }\r\n  \r\n  .takeaway-item:last-child {\r\n    margin-bottom: 0;\r\n  }\r\n  \r\n  .takeaway-number {\r\n    background-color: #3498db;\r\n    color: white;\r\n    width: 24px;\r\n    height: 24px;\r\n    border-radius: 50%;\r\n    display: flex;\r\n    align-items: center;\r\n    justify-content: center;\r\n    font-weight: 600;\r\n    margin-right: 1rem;\r\n    flex-shrink: 0;\r\n  }\r\n  \r\n  .takeaway-content {\r\n    flex-grow: 1;\r\n    padding-top: 0.25rem;\r\n  }\r\n  \r\n  \/* Responsive Styles *\/\r\n  @media (max-width: 768px) {\r\n    .rules-container, .examples-container, .mistakes-container, .applications-grid, .practice-tools, .visual-container {\r\n      grid-template-columns: 1fr;\r\n    }\r\n    \r\n    .interactive-inputs {\r\n      flex-direction: column;\r\n    }\r\n    \r\n    .article-title {\r\n      font-size: 2rem;\r\n    }\r\n    \r\n    .section-title {\r\n      font-size: 1.5rem;\r\n    }\r\n    \r\n    .intro-section, .understanding-section, .addition-rule-section, .examples-section, \r\n    .mistakes-section, .comparison-section, .applications-section, .practice-section, \r\n    .conclusion-section, .toc-section {\r\n      padding: 1.5rem;\r\n    }\r\n    \r\n    .table-header, .table-row {\r\n      grid-template-columns: 1fr;\r\n    }\r\n    \r\n    .table-header {\r\n      display: none;\r\n    }\r\n    \r\n    .table-cell {\r\n      padding: 0.75rem;\r\n    }\r\n    \r\n    .table-cell:first-child {\r\n      font-weight: 600;\r\n      background-color: #f8f9fa;\r\n    }\r\n    \r\n    .quiz-options {\r\n      grid-template-columns: 1fr;\r\n    }\r\n  }\r\n<\/style>\r\n\r\n<script>\r\n  document.addEventListener('DOMContentLoaded', function() {\r\n    \/\/ Significant Figures Visualization\r\n    const numberDisplay = document.getElementById('number-display');\r\n    const digitContainer = document.getElementById('digit-container');\r\n    const visualizationInput = document.getElementById('visualization-input');\r\n    const visualizeBtn = document.getElementById('visualize-btn');\r\n    \r\n    function visualizeNumber(number) {\r\n      \/\/ Clear previous visualization\r\n      digitContainer.innerHTML = '';\r\n      \r\n      const numStr = number.toString();\r\n      \r\n      for (let i = 0; i < numStr.length; i++) {\r\n        const digit = numStr[i];\r\n        const digitEl = document.createElement('div');\r\n        digitEl.style.width = '40px';\r\n        digitEl.style.height = '40px';\r\n        digitEl.style.display = 'flex';\r\n        digitEl.style.alignItems = 'center';\r\n        digitEl.style.justifyContent = 'center';\r\n        digitEl.style.margin = '0 2px';\r\n        digitEl.style.fontFamily = 'Courier New, monospace';\r\n        digitEl.style.fontWeight = '600';\r\n        digitEl.style.fontSize = '1.2rem';\r\n        digitEl.style.border = '1px solid #ced4da';\r\n        digitEl.textContent = digit;\r\n        \r\n        \/\/ Determine if significant\r\n        let isSignificant = false;\r\n        \r\n        if (digit === '.') {\r\n          \/\/ Decimal point is not a digit\r\n        } else if (digit !== '0') {\r\n          \/\/ Non-zero digits are always significant\r\n          isSignificant = true;\r\n        } else {\r\n          \/\/ Handle zeros\r\n          if (i > 0 && numStr[i-1] !== '.' && numStr[i-1] !== '0' && \r\n              (i < numStr.length - 1 && numStr[i+1] !== '0' && numStr[i+1] !== '.')) {\r\n            \/\/ Zero between non-zero digits\r\n            isSignificant = true;\r\n          } else if (numStr.includes('.') && i > numStr.indexOf('.')) {\r\n            \/\/ Zero after decimal point\r\n            if (i > numStr.indexOf('.') + 1 && numStr.slice(numStr.indexOf('.') + 1, i).replace(\/0\/g, '').length === 0) {\r\n              \/\/ Leading zeros after decimal point\r\n              if (i < numStr.length - 1 && numStr.slice(i+1).replace(\/0\/g, '').length > 0) {\r\n                \/\/ If there are non-zero digits after this\r\n                isSignificant = false;\r\n              } else {\r\n                \/\/ Trailing zeros after decimal point\r\n                isSignificant = true;\r\n              }\r\n            } else {\r\n              \/\/ Other zeros after decimal point\r\n              isSignificant = true;\r\n            }\r\n          } else if (i === numStr.length - 1 && !numStr.includes('.')) {\r\n            \/\/ Trailing zero without decimal point\r\n            isSignificant = false;\r\n          } else {\r\n            \/\/ Leading zeros\r\n            isSignificant = false;\r\n          }\r\n        }\r\n        \r\n        if (isSignificant) {\r\n          digitEl.style.backgroundColor = '#d4edda';\r\n          digitEl.style.borderColor = '#c3e6cb';\r\n        }\r\n        \r\n        digitContainer.appendChild(digitEl);\r\n      }\r\n      \r\n      \/\/ Add labels\r\n      const labelContainer = document.createElement('div');\r\n      labelContainer.style.display = 'flex';\r\n      labelContainer.style.justifyContent = 'center';\r\n      labelContainer.style.marginTop = '10px';\r\n      labelContainer.style.fontSize = '0.8rem';\r\n      labelContainer.style.color = '#6c757d';\r\n      \r\n      for (let i = 0; i < numStr.length; i++) {\r\n        const digit = numStr[i];\r\n        const labelEl = document.createElement('div');\r\n        labelEl.style.width = '40px';\r\n        labelEl.style.margin = '0 2px';\r\n        labelEl.style.textAlign = 'center';\r\n        \r\n        if (digit === '.') {\r\n          labelEl.textContent = '';\r\n        } else {\r\n          \/\/ Count decimal places\r\n          if (numStr.includes('.') && i > numStr.indexOf('.')) {\r\n            labelEl.textContent = (i - numStr.indexOf('.')) + ' dp';\r\n          } else {\r\n            labelEl.textContent = '';\r\n          }\r\n        }\r\n        \r\n        labelContainer.appendChild(labelEl);\r\n      }\r\n      \r\n      digitContainer.appendChild(labelContainer);\r\n    }\r\n    \r\n    visualizeBtn.addEventListener('click', function() {\r\n      const number = visualizationInput.value;\r\n      if (!number || isNaN(parseFloat(number))) {\r\n        alert('Please enter a valid number');\r\n        return;\r\n      }\r\n      \r\n      numberDisplay.textContent = number;\r\n      visualizeNumber(number);\r\n    });\r\n    \r\n    \/\/ Initialize with default value\r\n    visualizeNumber('12.340');\r\n    \r\n    \/\/ Interactive Example Calculator\r\n    const number1Input = document.getElementById('number1');\r\n    const number2Input = document.getElementById('number2');\r\n    const operationSelect = document.getElementById('operation');\r\n    const calculateBtn = document.getElementById('calculate-btn');\r\n    const rawResult = document.getElementById('raw-result');\r\n    const sigFigResult = document.getElementById('sig-fig-result');\r\n    const resultExplanation = document.getElementById('result-explanation');\r\n    \r\n    calculateBtn.addEventListener('click', function() {\r\n      const num1 = parseFloat(number1Input.value);\r\n      const num2 = parseFloat(number2Input.value);\r\n      const operation = operationSelect.value;\r\n      \r\n      if (isNaN(num1) || isNaN(num2)) {\r\n        rawResult.textContent = 'Invalid input';\r\n        sigFigResult.textContent = 'Invalid input';\r\n        resultExplanation.textContent = 'Please enter valid numbers';\r\n        return;\r\n      }\r\n      \r\n      \/\/ Perform calculation\r\n      let result;\r\n      if (operation === 'add') {\r\n        result = num1 + num2;\r\n      } else {\r\n        result = num1 - num2;\r\n      }\r\n      \r\n      rawResult.textContent = result;\r\n      \r\n      \/\/ Determine decimal places\r\n      const dp1 = (number1Input.value.split('.')[1] || '').length;\r\n      const dp2 = (number2Input.value.split('.')[1] || '').length;\r\n      const minDP = Math.min(dp1, dp2);\r\n      \r\n      \/\/ Round to the correct number of decimal places\r\n      const roundedResult = result.toFixed(minDP);\r\n      sigFigResult.textContent = roundedResult;\r\n      \r\n      \/\/ Generate explanation\r\n      resultExplanation.textContent = `${number1Input.value} has ${dp1} decimal places, ${number2Input.value} has ${dp2} decimal places. The result is rounded to ${minDP} decimal places (the fewest).`;\r\n    });\r\n    \r\n    \/\/ Quiz functionality\r\n    const quizQuestions = [\r\n      {\r\n        question: \"Which of the following is correctly rounded according to significant figure rules for addition?\",\r\n        options: [\r\n          { text: \"12.37 + 5.8 = 18.17\", correct: false },\r\n          { text: \"12.37 + 5.8 = 18.2\", correct: true },\r\n          { text: \"12.37 + 5.8 = 18\", correct: false },\r\n          { text: \"12.37 + 5.8 = 18.17 (3 sig figs)\", correct: false }\r\n        ],\r\n        explanation: \"When adding, the result should have the same number of decimal places as the measurement with the fewest decimal places. 5.8 has 1 decimal place, so the result should be rounded to 1 decimal place: 18.2\"\r\n      },\r\n      {\r\n        question: \"What is the correct result for 100 + 23.45 using significant figure rules?\",\r\n        options: [\r\n          { text: \"123.45\", correct: false },\r\n          { text: \"123.5\", correct: false },\r\n          { text: \"123\", correct: true },\r\n          { text: \"120\", correct: false }\r\n        ],\r\n        explanation: \"100 has 0 decimal places, so the result should be rounded to 0 decimal places: 123\"\r\n      },\r\n      {\r\n        question: \"Which rule applies to addition and subtraction with significant figures?\",\r\n        options: [\r\n          { text: \"Round to the same number of significant figures as the measurement with the fewest significant figures\", correct: false },\r\n          { text: \"Round to the same number of decimal places as the measurement with the fewest decimal places\", correct: true },\r\n          { text: \"Always round to 3 significant figures\", correct: false },\r\n          { text: \"Keep all digits in the final answer\", correct: false }\r\n        ],\r\n        explanation: \"For addition and subtraction, we round to the same number of decimal places as the measurement with the fewest decimal places.\"\r\n      }\r\n    ];\r\n    \r\n    let currentQuizQuestion = 0;\r\n    const quizQuestion = document.getElementById('quiz-question');\r\n    const quizOptions = document.querySelector('.quiz-options');\r\n    const quizFeedback = document.getElementById('quiz-feedback');\r\n    const quizNext = document.getElementById('quiz-next');\r\n    \r\n    function loadQuizQuestion() {\r\n      const question = quizQuestions[currentQuizQuestion];\r\n      quizQuestion.textContent = question.question;\r\n      \r\n      \/\/ Clear previous options\r\n      quizOptions.innerHTML = '';\r\n      \r\n      \/\/ Add new options\r\n      question.options.forEach(option => {\r\n        const button = document.createElement('button');\r\n        button.className = 'quiz-option';\r\n        button.textContent = option.text;\r\n        button.dataset.correct = option.correct;\r\n        button.addEventListener('click', checkQuizAnswer);\r\n        quizOptions.appendChild(button);\r\n      });\r\n      \r\n      quizFeedback.textContent = '';\r\n      quizFeedback.style.color = '';\r\n      quizNext.style.display = 'none';\r\n    }\r\n    \r\n    function checkQuizAnswer(e) {\r\n      const selectedOption = e.target;\r\n      const isCorrect = selectedOption.dataset.correct === 'true';\r\n      \r\n      \/\/ Disable all options\r\n      document.querySelectorAll('.quiz-option').forEach(option => {\r\n        option.disabled = true;\r\n        \r\n        if (option.dataset.correct === 'true') {\r\n          option.style.backgroundColor = '#d4edda';\r\n          option.style.borderColor = '#c3e6cb';\r\n        }\r\n      });\r\n      \r\n      if (isCorrect) {\r\n        quizFeedback.textContent = 'Correct! ' + quizQuestions[currentQuizQuestion].explanation;\r\n        quizFeedback.style.color = '#28a745';\r\n        selectedOption.style.backgroundColor = '#d4edda';\r\n        selectedOption.style.borderColor = '#c3e6cb';\r\n      } else {\r\n        quizFeedback.textContent = 'Incorrect. ' + quizQuestions[currentQuizQuestion].explanation;\r\n        quizFeedback.style.color = '#dc3545';\r\n        selectedOption.style.backgroundColor = '#f8d7da';\r\n        selectedOption.style.borderColor = '#f5c6cb';\r\n      }\r\n      \r\n      quizNext.style.display = 'block';\r\n    }\r\n    \r\n    quizNext.addEventListener('click', function() {\r\n      currentQuizQuestion = (currentQuizQuestion + 1) % quizQuestions.length;\r\n      loadQuizQuestion();\r\n    });\r\n    \r\n    \/\/ Initialize quiz\r\n    loadQuizQuestion();\r\n    \r\n    \/\/ Multi-number calculator\r\n    const multiInputContainer = document.getElementById('multi-input-container');\r\n    const addNumberBtn = document.getElementById('add-number-btn');\r\n    const multiCalculateBtn = document.getElementById('multi-calculate-btn');\r\n    const multiRawResult = document.getElementById('multi-raw-result');\r\n    const multiSigFigResult = document.getElementById('multi-sig-fig-result');\r\n    const multiResultExplanation = document.getElementById('multi-result-explanation');\r\n    \r\n    addNumberBtn.addEventListener('click', function() {\r\n      const newRow = document.createElement('div');\r\n      newRow.className = 'input-row';\r\n      \r\n      const newInput = document.createElement('input');\r\n      newInput.type = 'text';\r\n      newInput.className = 'number-input';\r\n      newInput.placeholder = 'Enter a number';\r\n      \r\n      const newSelect = document.createElement('select');\r\n      newSelect.className = 'operation-select';\r\n      \r\n      const addOption = document.createElement('option');\r\n      addOption.value = 'add';\r\n      addOption.textContent = '+';\r\n      \r\n      const subtractOption = document.createElement('option');\r\n      subtractOption.value = 'subtract';\r\n      subtractOption.textContent = '-';\r\n      \r\n      newSelect.appendChild(addOption);\r\n      newSelect.appendChild(subtractOption);\r\n      \r\n      const removeBtn = document.createElement('button');\r\n      removeBtn.className = 'remove-btn';\r\n      removeBtn.textContent = '\u00d7';\r\n      removeBtn.addEventListener('click', function() {\r\n        multiInputContainer.removeChild(newRow);\r\n      });\r\n      \r\n      newRow.appendChild(newInput);\r\n      newRow.appendChild(newSelect);\r\n      newRow.appendChild(removeBtn);\r\n      \r\n      \/\/ Insert before the last row\r\n      multiInputContainer.insertBefore(newRow, multiInputContainer.lastElementChild);\r\n    });\r\n    \r\n    multiCalculateBtn.addEventListener('click', function() {\r\n      const inputs = multiInputContainer.querySelectorAll('.number-input');\r\n      const operations = multiInputContainer.querySelectorAll('.operation-select');\r\n      \r\n      if (inputs.length < 2) {\r\n        multiRawResult.textContent = 'Need at least two numbers';\r\n        multiSigFigResult.textContent = '-';\r\n        multiResultExplanation.textContent = '';\r\n        return;\r\n      }\r\n      \r\n      \/\/ Collect numbers and operations\r\n      const numbers = [];\r\n      const ops = [];\r\n      let minDecimalPlaces = Infinity;\r\n      \r\n      for (let i = 0; i < inputs.length; i++) {\r\n        const value = inputs[i].value;\r\n        if (!value || isNaN(parseFloat(value))) {\r\n          multiRawResult.textContent = 'Invalid input';\r\n          multiSigFigResult.textContent = '-';\r\n          multiResultExplanation.textContent = 'Please enter valid numbers';\r\n          return;\r\n        }\r\n        \r\n        numbers.push(parseFloat(value));\r\n        \r\n        \/\/ Determine decimal places\r\n        const decimalPlaces = (value.split('.')[1] || '').length;\r\n        minDecimalPlaces = Math.min(minDecimalPlaces, decimalPlaces);\r\n        \r\n        \/\/ Get operation (except for the last number)\r\n        if (i < inputs.length - 1) {\r\n          ops.push(operations[i].value);\r\n        }\r\n      }\r\n      \r\n      \/\/ Calculate result\r\n      let result = numbers[0];\r\n      for (let i = 0; i < ops.length; i++) {\r\n        if (ops[i] === 'add') {\r\n          result += numbers[i + 1];\r\n        } else {\r\n          result -= numbers[i + 1];\r\n        }\r\n      }\r\n      \r\n      multiRawResult.textContent = result;\r\n      \r\n      \/\/ Round to the correct number of decimal places\r\n      const roundedResult = result.toFixed(minDecimalPlaces);\r\n      multiSigFigResult.textContent = roundedResult;\r\n      \r\n      \/\/ Generate explanation\r\n      multiResultExplanation.textContent = `The number with the fewest decimal places has ${minDecimalPlaces} decimal places. The result is rounded to ${minDecimalPlaces} decimal places.`;\r\n    });\r\n    \r\n    \/\/ Practice problems\r\n    const practiceProblems = [\r\n      {\r\n        problem: \"Calculate 23.45 + 6.7 with the correct number of significant figures.\",\r\n        answer: \"30.2\"\r\n      },\r\n      {\r\n        problem: \"Calculate 100 - 12.34 with the correct number of significant figures.\",\r\n        answer: \"88\"\r\n      },\r\n      {\r\n        problem: \"Calculate 5.678 + 9.1 + 2.34 with the correct number of significant figures.\",\r\n        answer: \"17.1\"\r\n      },\r\n      {\r\n        problem: \"Calculate 45.67 - 5 with the correct number of significant figures.\",\r\n        answer: \"41\"\r\n      },\r\n      {\r\n        problem: \"Calculate 0.0025 + 1.3 with the correct number of significant figures.\",\r\n        answer: \"1.3\"\r\n      }\r\n    ];\r\n    \r\n    let currentProblem = 0;\r\n    let correctCount = 0;\r\n    let totalAttempted = 0;\r\n    \r\n    const problemText = document.getElementById('problem-text');\r\n    const problemAnswer = document.getElementById('problem-answer');\r\n    const checkAnswerBtn = document.getElementById('check-answer-btn');\r\n    const problemFeedback = document.getElementById('problem-feedback');\r\n    const nextProblemBtn = document.getElementById('next-problem-btn');\r\n    const progressFill = document.getElementById('progress-fill');\r\n    const correctCountEl = document.getElementById('correct-count');\r\n    const totalAttemptedEl = document.getElementById('total-attempted');\r\n    \r\n    function loadProblem() {\r\n      const problem = practiceProblems[currentProblem];\r\n      problemText.textContent = problem.problem;\r\n      problemAnswer.value = '';\r\n      problemFeedback.textContent = '';\r\n      problemFeedback.style.color = '';\r\n      nextProblemBtn.style.display = 'none';\r\n      \r\n      \/\/ Update problem number\r\n      document.querySelector('.problem-number').textContent = `Problem ${currentProblem + 1} of ${practiceProblems.length}`;\r\n      \r\n      \/\/ Update progress bar\r\n      const progressPercent = ((currentProblem + 1) \/ practiceProblems.length) * 100;\r\n      progressFill.style.width = `${progressPercent}%`;\r\n    }\r\n    \r\n    checkAnswerBtn.addEventListener('click', function() {\r\n      const userAnswer = problemAnswer.value.trim();\r\n      const correctAnswer = practiceProblems[currentProblem].answer;\r\n      \r\n      if (!userAnswer) {\r\n        problemFeedback.textContent = 'Please enter an answer';\r\n        problemFeedback.style.color = '#dc3545';\r\n        return;\r\n      }\r\n      \r\n      totalAttempted++;\r\n      totalAttemptedEl.textContent = totalAttempted;\r\n      \r\n      if (userAnswer === correctAnswer) {\r\n        problemFeedback.textContent = 'Correct!';\r\n        problemFeedback.style.color = '#28a745';\r\n        correctCount++;\r\n        correctCountEl.textContent = correctCount;\r\n      } else {\r\n        problemFeedback.textContent = `Incorrect. The correct answer is ${correctAnswer}.`;\r\n        problemFeedback.style.color = '#dc3545';\r\n      }\r\n      \r\n      nextProblemBtn.style.display = 'block';\r\n    });\r\n    \r\n    nextProblemBtn.addEventListener('click', function() {\r\n      currentProblem = (currentProblem + 1) % practiceProblems.length;\r\n      loadProblem();\r\n    });\r\n    \r\n    \/\/ Decimal Places Visualizer\r\n    const decimalInput = document.getElementById('decimal-input');\r\n    const visualizeDecimalBtn = document.getElementById('visualize-decimal-btn');\r\n    const decimalVisualization = document.getElementById('decimal-visualization');\r\n    \r\n    visualizeDecimalBtn.addEventListener('click', function() {\r\n      const number = decimalInput.value;\r\n      if (!number || isNaN(parseFloat(number))) {\r\n        decimalVisualization.innerHTML = '<div class=\"placeholder-text\">Please enter a valid number<\/div>';\r\n        return;\r\n      }\r\n      \r\n      \/\/ Clear previous visualization\r\n      decimalVisualization.innerHTML = '';\r\n      \r\n      const numStr = number.toString();\r\n      const hasDecimal = numStr.includes('.');\r\n      const decimalPlaces = hasDecimal ? numStr.split('.')[1].length : 0;\r\n      \r\n      \/\/ Create visualization\r\n      const container = document.createElement('div');\r\n      \r\n      \/\/ Number representation\r\n      const numberRep = document.createElement('div');\r\n      numberRep.style.fontSize = '2rem';\r\n      numberRep.style.fontWeight = '600';\r\n      numberRep.style.fontFamily = 'Courier New, monospace';\r\n      numberRep.style.textAlign = 'center';\r\n      numberRep.style.marginBottom = '1rem';\r\n      numberRep.textContent = numStr;\r\n      \r\n      \/\/ Decimal places info\r\n      const decimalInfo = document.createElement('div');\r\n      decimalInfo.style.textAlign = 'center';\r\n      decimalInfo.style.marginBottom = '1.5rem';\r\n      \r\n      if (hasDecimal) {\r\n        decimalInfo.innerHTML = `This number has <span style=\"font-weight: 600; color: #3498db;\">${decimalPlaces} decimal places<\/span>`;\r\n      } else {\r\n        decimalInfo.innerHTML = `This number has <span style=\"font-weight: 600; color: #3498db;\">0 decimal places<\/span> (it's a whole number)`;\r\n      }\r\n      \r\n      \/\/ Visual representation\r\n      const visualRep = document.createElement('div');\r\n      visualRep.style.display = 'flex';\r\n      visualRep.style.justifyContent = 'center';\r\n      visualRep.style.marginBottom = '1rem';\r\n      \r\n      for (let i = 0; i < numStr.length; i++) {\r\n        const digit = numStr[i];\r\n        const digitBox = document.createElement('div');\r\n        digitBox.style.width = '40px';\r\n        digitBox.style.height = '40px';\r\n        digitBox.style.display = 'flex';\r\n        digitBox.style.alignItems = 'center';\r\n        digitBox.style.justifyContent = 'center';\r\n        digitBox.style.margin = '0 2px';\r\n        digitBox.style.border = '1px solid #ced4da';\r\n        digitBox.style.fontFamily = 'Courier New, monospace';\r\n        digitBox.style.fontWeight = '600';\r\n        digitBox.style.fontSize = '1.2rem';\r\n        digitBox.textContent = digit;\r\n        \r\n        \/\/ Highlight decimal places\r\n        if (hasDecimal && i > numStr.indexOf('.')) {\r\n          digitBox.style.backgroundColor = '#e8f4f8';\r\n          digitBox.style.borderColor = '#bee5eb';\r\n        }\r\n        \r\n        visualRep.appendChild(digitBox);\r\n      }\r\n      \r\n      \/\/ Labels for decimal places\r\n      const labels = document.createElement('div');\r\n      labels.style.display = 'flex';\r\n      labels.style.justifyContent = 'center';\r\n      \r\n      for (let i = 0; i < numStr.length; i++) {\r\n        const label = document.createElement('div');\r\n        label.style.width = '40px';\r\n        label.style.margin = '0 2px';\r\n        label.style.textAlign = 'center';\r\n        label.style.fontSize = '0.8rem';\r\n        label.style.color = '#6c757d';\r\n        \r\n        if (hasDecimal && i > numStr.indexOf('.')) {\r\n          label.textContent = `${i - numStr.indexOf('.')}${getOrdinalSuffix(i - numStr.indexOf('.'))}`;\r\n          label.style.fontWeight = '500';\r\n          label.style.color = '#3498db';\r\n        }\r\n        \r\n        labels.appendChild(label);\r\n      }\r\n      \r\n      \/\/ Addition rule explanation\r\n      const explanation = document.createElement('div');\r\n      explanation.style.marginTop = '2rem';\r\n      explanation.style.padding = '1rem';\r\n      explanation.style.backgroundColor = '#e8f4f8';\r\n      explanation.style.borderRadius = '4px';\r\n      \r\n      explanation.innerHTML = `\r\n        <div style=\"font-weight: 600; margin-bottom: 0.5rem;\">Addition Rule:<\/div>\r\n        <div>When adding or subtracting this number with another number, the result should be rounded to match the number with the fewest decimal places.<\/div>\r\n        <div style=\"margin-top: 0.5rem;\">This number has <span style=\"font-weight: 600;\">${decimalPlaces} decimal places<\/span>.<\/div>\r\n      `;\r\n      \r\n      container.appendChild(numberRep);\r\n      container.appendChild(decimalInfo);\r\n      container.appendChild(visualRep);\r\n      container.appendChild(labels);\r\n      container.appendChild(explanation);\r\n      \r\n      decimalVisualization.appendChild(container);\r\n    });\r\n    \r\n    function getOrdinalSuffix(num) {\r\n      const j = num % 10;\r\n      const k = num % 100;\r\n      \r\n      if (j === 1 && k !== 11) {\r\n        return 'st';\r\n      }\r\n      if (j === 2 && k !== 12) {\r\n        return 'nd';\r\n      }\r\n      if (j === 3 && k !== 13) {\r\n        return 'rd';\r\n      }\r\n      return 'th';\r\n    }\r\n    \r\n    \/\/ Initialize practice problem\r\n    loadProblem();\r\n    \r\n    \/\/ Smooth scrolling for anchor links\r\n    document.querySelectorAll('a[href^=\"#\"]').forEach(anchor => {\r\n      anchor.addEventListener('click', function(e) {\r\n        e.preventDefault();\r\n        \r\n        const targetId = this.getAttribute('href');\r\n        const targetElement = document.querySelector(targetId);\r\n        \r\n        if (targetElement) {\r\n          window.scrollTo({\r\n            top: targetElement.offsetTop - 20,\r\n            behavior: 'smooth'\r\n          });\r\n        }\r\n      });\r\n    });\r\n  });\r\n<\/script>\r\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":5,"featured_media":5332,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[43],"tags":[],"class_list":["post-5364","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tips-tricks"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Quando si aggiunge, quante cifre significative? - Calcolatore di cifre significative<\/title>\n<meta name=\"description\" content=\"Nell&#039;ambito dei calcoli scientifici, ingegneristici e matematici, le cifre significative svolgono un ruolo cruciale nell&#039;espressione...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sigfigcalculator.io\/it\/how-many-sig-figs\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"When adding, how many sig figs? - SigFig Calculator\" \/>\n<meta property=\"og:description\" content=\"When performing calculations in science, engineering, and mathematics, significant figures (sig figs) play a crucial role in expressing...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/\" \/>\n<meta property=\"og:site_name\" content=\"SigFig Calculator\" \/>\n<meta property=\"article:published_time\" content=\"2025-05-13T05:53:07+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-05-13T11:38:25+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/sigfigcalculator.io\/wp-content\/uploads\/2025\/05\/cal_blog2.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"900\" \/>\n\t<meta property=\"og:image:height\" content=\"600\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Mildred Perry\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mildred Perry\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/\"},\"author\":{\"name\":\"Mildred Perry\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/#\\\/schema\\\/person\\\/2a0e04c0561c19c0ec7767d6c62e1d8f\"},\"headline\":\"When adding, how many sig figs?\",\"datePublished\":\"2025-05-13T05:53:07+00:00\",\"dateModified\":\"2025-05-13T11:38:25+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/\"},\"wordCount\":9,\"commentCount\":0,\"image\":{\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/sigfigcalculator.io\\\/wp-content\\\/uploads\\\/2025\\\/05\\\/cal_blog2.jpg\",\"articleSection\":[\"Tips &amp; Tricks\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/\",\"url\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/\",\"name\":\"When adding, how many sig figs? - SigFig Calculator\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/sigfigcalculator.io\\\/wp-content\\\/uploads\\\/2025\\\/05\\\/cal_blog2.jpg\",\"datePublished\":\"2025-05-13T05:53:07+00:00\",\"dateModified\":\"2025-05-13T11:38:25+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/#\\\/schema\\\/person\\\/2a0e04c0561c19c0ec7767d6c62e1d8f\"},\"description\":\"When performing calculations in science, engineering, and mathematics, significant figures (sig figs) play a crucial role in expressing...\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/#primaryimage\",\"url\":\"https:\\\/\\\/sigfigcalculator.io\\\/wp-content\\\/uploads\\\/2025\\\/05\\\/cal_blog2.jpg\",\"contentUrl\":\"https:\\\/\\\/sigfigcalculator.io\\\/wp-content\\\/uploads\\\/2025\\\/05\\\/cal_blog2.jpg\",\"width\":900,\"height\":600},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/how-many-sig-figs\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/sigfigcalculator.io\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"When adding, how many sig figs?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/#website\",\"url\":\"https:\\\/\\\/sigfigcalculator.io\\\/\",\"name\":\"SigFig Calculator\",\"description\":\"Your tool for perfect scientific accuracy\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/sigfigcalculator.io\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/#\\\/schema\\\/person\\\/2a0e04c0561c19c0ec7767d6c62e1d8f\",\"name\":\"Mildred Perry\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/wp-content\\\/uploads\\\/2025\\\/05\\\/Mildred-Perry-96x96.png\",\"url\":\"https:\\\/\\\/sigfigcalculator.io\\\/wp-content\\\/uploads\\\/2025\\\/05\\\/Mildred-Perry-96x96.png\",\"contentUrl\":\"https:\\\/\\\/sigfigcalculator.io\\\/wp-content\\\/uploads\\\/2025\\\/05\\\/Mildred-Perry-96x96.png\",\"caption\":\"Mildred Perry\"},\"description\":\"Mildred Perry is a computer science engineer (CSE) turned tech blogger who combines hands-on development experience with a talent for clear, insightful writing. Drawing on her expertise in algorithms, software architecture, and emerging technologies, she authors in-depth tutorials and analysis on topics ranging from full-stack development to machine learning. Mildred\u2019s engaging, example-driven posts help both novice and experienced developers tackle real-world challenges and stay current in a fast-moving field.\",\"url\":\"https:\\\/\\\/sigfigcalculator.io\\\/it\\\/author\\\/mildredperry\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Quando si aggiunge, quante cifre significative? - Calcolatore di cifre significative","description":"Nell&#39;ambito dei calcoli scientifici, ingegneristici e matematici, le cifre significative svolgono un ruolo cruciale nell&#39;espressione...","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sigfigcalculator.io\/it\/how-many-sig-figs\/","og_locale":"en_US","og_type":"article","og_title":"When adding, how many sig figs? - SigFig Calculator","og_description":"When performing calculations in science, engineering, and mathematics, significant figures (sig figs) play a crucial role in expressing...","og_url":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/","og_site_name":"SigFig Calculator","article_published_time":"2025-05-13T05:53:07+00:00","article_modified_time":"2025-05-13T11:38:25+00:00","og_image":[{"width":900,"height":600,"url":"https:\/\/sigfigcalculator.io\/wp-content\/uploads\/2025\/05\/cal_blog2.jpg","type":"image\/jpeg"}],"author":"Mildred Perry","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Mildred Perry","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/#article","isPartOf":{"@id":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/"},"author":{"name":"Mildred Perry","@id":"https:\/\/sigfigcalculator.io\/#\/schema\/person\/2a0e04c0561c19c0ec7767d6c62e1d8f"},"headline":"When adding, how many sig figs?","datePublished":"2025-05-13T05:53:07+00:00","dateModified":"2025-05-13T11:38:25+00:00","mainEntityOfPage":{"@id":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/"},"wordCount":9,"commentCount":0,"image":{"@id":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/#primaryimage"},"thumbnailUrl":"https:\/\/sigfigcalculator.io\/wp-content\/uploads\/2025\/05\/cal_blog2.jpg","articleSection":["Tips &amp; Tricks"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/sigfigcalculator.io\/how-many-sig-figs\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/","url":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/","name":"When adding, how many sig figs? - SigFig Calculator","isPartOf":{"@id":"https:\/\/sigfigcalculator.io\/#website"},"primaryImageOfPage":{"@id":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/#primaryimage"},"image":{"@id":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/#primaryimage"},"thumbnailUrl":"https:\/\/sigfigcalculator.io\/wp-content\/uploads\/2025\/05\/cal_blog2.jpg","datePublished":"2025-05-13T05:53:07+00:00","dateModified":"2025-05-13T11:38:25+00:00","author":{"@id":"https:\/\/sigfigcalculator.io\/#\/schema\/person\/2a0e04c0561c19c0ec7767d6c62e1d8f"},"description":"When performing calculations in science, engineering, and mathematics, significant figures (sig figs) play a crucial role in expressing...","breadcrumb":{"@id":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sigfigcalculator.io\/how-many-sig-figs\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/#primaryimage","url":"https:\/\/sigfigcalculator.io\/wp-content\/uploads\/2025\/05\/cal_blog2.jpg","contentUrl":"https:\/\/sigfigcalculator.io\/wp-content\/uploads\/2025\/05\/cal_blog2.jpg","width":900,"height":600},{"@type":"BreadcrumbList","@id":"https:\/\/sigfigcalculator.io\/how-many-sig-figs\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/sigfigcalculator.io\/"},{"@type":"ListItem","position":2,"name":"When adding, how many sig figs?"}]},{"@type":"WebSite","@id":"https:\/\/sigfigcalculator.io\/#website","url":"https:\/\/sigfigcalculator.io\/","name":"SigFig Calculator","description":"Your tool for perfect scientific accuracy","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sigfigcalculator.io\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/sigfigcalculator.io\/#\/schema\/person\/2a0e04c0561c19c0ec7767d6c62e1d8f","name":"Mildred Perry","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/sigfigcalculator.io\/wp-content\/uploads\/2025\/05\/Mildred-Perry-96x96.png","url":"https:\/\/sigfigcalculator.io\/wp-content\/uploads\/2025\/05\/Mildred-Perry-96x96.png","contentUrl":"https:\/\/sigfigcalculator.io\/wp-content\/uploads\/2025\/05\/Mildred-Perry-96x96.png","caption":"Mildred Perry"},"description":"Mildred Perry is a computer science engineer (CSE) turned tech blogger who combines hands-on development experience with a talent for clear, insightful writing. Drawing on her expertise in algorithms, software architecture, and emerging technologies, she authors in-depth tutorials and analysis on topics ranging from full-stack development to machine learning. Mildred\u2019s engaging, example-driven posts help both novice and experienced developers tackle real-world challenges and stay current in a fast-moving field.","url":"https:\/\/sigfigcalculator.io\/it\/author\/mildredperry\/"}]}},"_links":{"self":[{"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/posts\/5364","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/comments?post=5364"}],"version-history":[{"count":1,"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/posts\/5364\/revisions"}],"predecessor-version":[{"id":5365,"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/posts\/5364\/revisions\/5365"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/media\/5332"}],"wp:attachment":[{"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/media?parent=5364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/categories?post=5364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sigfigcalculator.io\/it\/wp-json\/wp\/v2\/tags?post=5364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}