Using The Rules of Significant Figures Calculate The Following 4.0021-0.839

How to Calculate 4.0021-0.839 with Significant Figures

The rules of significant figures are essential for maintaining accuracy in scientific measurements. When subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places in the original calculation.

Step-by-Step Calculation

1. Identify the number of significant figures in each operand:
   • 4.0021 has 5 significant figures
   • 0.839 has 3 significant figures
2. Perform the subtraction:

   4.0021 - 0.839 = 3.1631

3. Apply the significant figures rule:
   • The number with the fewest decimal places is 0.839 (3 decimal places)
   • Round the result to 3 decimal places: 3.163

Step-by-Step Calculation

Let's break down the calculation of 4.0021 - 0.839 with significant figures:

1. First, align the decimal points:

   4.0021
   - 0.839
   -------
   3.1631

2. Now, count the decimal places in each number:
   • 4.0021 has 4 decimal places
   • 0.839 has 3 decimal places
3. According to the rules, the result should have the same number of decimal places as the number with the fewest decimal places (0.839 has 3 decimal places).
4. Round the result to 3 decimal places:
   • 3.1631 becomes 3.163 when rounded to 3 decimal places

The final result with proper significant figures is 3.163.

Common Mistakes to Avoid

When working with significant figures, it's easy to make mistakes. Here are some common errors to watch out for:

• Ignoring trailing zeros: Numbers like 4.0021 have trailing zeros that are significant, while 4.00210 might have more significant figures.
• Counting leading zeros: Leading zeros (zeros before the first non-zero digit) are not significant. For example, 0.0045 has 2 significant figures.
• Rounding too early: Always perform calculations first, then round the final result to the appropriate number of significant figures.
• Misapplying rules: Remember that multiplication and division follow different rules than addition and subtraction.

Practical Example

Let's look at a practical example to see how significant figures work in a real-world scenario.

Example Problem

A chemistry student measures two solutions:

• Solution A: 4.0021 grams
• Solution B: 0.839 grams

The student needs to find the difference in mass between the two solutions.

Solution

1. First, perform the subtraction:

   4.0021 g - 0.839 g = 3.1631 g

2. Count the significant figures:
   • 4.0021 has 5 significant figures
   • 0.839 has 3 significant figures
3. Apply the significant figures rule:

   The result should have the same number of decimal places as the number with the fewest decimal places (0.839 has 3 decimal places).

4. Round the result to 3 decimal places:

   3.1631 g becomes 3.163 g

The final answer is 3.163 grams, which properly accounts for significant figures.