Calculate 0.82 0.042 4.4 103 Keeping Only Significant Figures

When performing calculations with measured numbers, it's important to maintain proper significant figures to ensure accurate and meaningful results. This guide explains how to calculate with 0.82, 0.042, 4.4, and 103 while keeping only significant figures.

Introduction

Significant figures, also known as significant digits, are the meaningful digits in a number that carry information about the precision of the measurement. When performing calculations, the number of significant figures in the final result should be based on the least precise measurement in the calculation.

In this example, we'll calculate with the numbers 0.82, 0.042, 4.4, and 103, and determine the result while keeping only the significant figures.

How to Calculate with Significant Figures

To calculate with significant figures, follow these steps:

Identify the number of significant figures in each number.
Perform the calculation as usual.
Round the final result to the same number of significant figures as the least precise number in the calculation.

Remember: Zeros between non-zero digits are always significant. Zeros at the beginning or end of a number may or may not be significant depending on the context.

Example: Counting Significant Figures

Let's examine each number:

0.82 - 2 significant figures (the zero is not significant)
0.042 - 3 significant figures (the zeros are not significant)
4.4 - 2 significant figures (the zero is significant)
103 - 3 significant figures (the zero is significant)

The least precise number in this set is 0.82 and 4.4, each with 2 significant figures. Therefore, the final result should be rounded to 2 significant figures.

Example Calculation

Let's perform a sample calculation with these numbers. Suppose we want to calculate the sum of 0.82, 0.042, 4.4, and 103.

0.82 + 0.042 + 4.4 + 103 = 108.262

Now, we round 108.262 to 2 significant figures:

108.262 → 110 (rounded to 2 significant figures)

The final result is 110 when keeping only significant figures.

Common Mistakes

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

Counting trailing zeros as significant when they are not.
Rounding too early in a calculation.
Forgetting to round the final result to the correct number of significant figures.

To ensure accuracy, always double-check your significant figure count and apply rounding at the appropriate stage of the calculation.

Frequently Asked Questions

How do I determine the number of significant figures in a number?: Count all non-zero digits and any trailing zeros that are after the decimal point. Leading zeros are not significant.
What if I have numbers with different numbers of significant figures?: The final result should be rounded to the same number of significant figures as the least precise number in the calculation.
Can I add or subtract significant figures?: No, significant figures are not added or subtracted. They are determined by the precision of the measurement.
What if I have a number like 0.00050?: In this case, the trailing zeros are significant, so 0.00050 has 5 significant figures.
How do I handle multiplication and division with significant figures?: For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures in the calculation.