Sing The Rules of Significant Figures Calculate The Following 4.0021-0.247

This guide explains how to properly apply significant figures rules when calculating 4.0021 - 0.247. We'll cover the rules, show a worked example, and provide a calculator for quick calculations.

Introduction

Significant figures (also called significant digits) are the meaningful digits in a number that carry precise information. When performing calculations, it's important to maintain the correct number of significant figures to ensure accurate results.

In this example, we'll calculate 4.0021 - 0.247 while properly applying significant figures rules.

Significant Figures Rules

Rule 1: Non-zero digits are always significant

All non-zero digits in a number are significant. For example, in 4.0021, the digits 4, 0, 0, 2, and 1 are all significant.

Rule 2: Any zeros between non-zero digits are significant

Zeros that appear between non-zero digits are significant. In 4.0021, the zeros between the 4 and the 2 are significant.

Rule 3: Leading zeros are not significant

Leading zeros (zeros before the first non-zero digit) are not significant. For example, in 0.247, the zero is not significant.

Rule 4: Trailing zeros in a decimal number are significant

Zeros at the end of a number after the decimal point are significant. In 0.247, all digits are significant.

Rule 5: Trailing zeros in a whole number may or may not be significant

If the number has a decimal point, trailing zeros are significant. If there's no decimal point, trailing zeros may or may not be significant. For example, 2470 could have 1, 2, 3, or 4 significant figures depending on the context.

Key Formula

The result of a calculation should have the same number of significant figures as the least precise measurement in the calculation.

Calculation Example

Let's calculate 4.0021 - 0.247 with proper significant figures.

Step 1: Identify significant figures in each number

4.0021 has 5 significant figures
0.247 has 3 significant figures

Step 2: Perform the calculation

4.0021 - 0.247 = 3.7551

Step 3: Apply significant figures rule

The result should have the same number of significant figures as the least precise measurement, which is 3 significant figures.

Final Result

3.76 (rounded to 3 significant figures)

Note: The result is rounded to 3 significant figures because 0.247 has only 3 significant figures.

Common Mistakes

Mistake 1: Ignoring significant figures

Some people might calculate 4.0021 - 0.247 = 3.7551 and not round it, which would be incorrect.

Mistake 2: Counting trailing zeros incorrectly

If you mistakenly count trailing zeros in 0.247 as significant, you might round to 4 significant figures instead of 3.

Mistake 3: Rounding before subtracting

Some people might round 4.0021 to 4.002 before subtracting, which would give an incorrect intermediate result.

FAQ

How many significant figures should the result have?

The result should have the same number of significant figures as the least precise measurement in the calculation. In this case, 0.247 has 3 significant figures, so the result should have 3 significant figures.

What if both numbers have the same number of significant figures?

If both numbers have the same number of significant figures, the result should have that same number of significant figures.

How do I count significant figures in a number?

Count all non-zero digits and any zeros between non-zero digits. Leading zeros are not significant, and trailing zeros in a whole number may or may not be significant unless there's a decimal point.