October 11, 2025

How To Apply Significant Figures Addition Subtraction

Q: Is this rule different from multiplication and division?

Yes, for multiplication and division, the result is rounded to the same number of significant figures as the measurement with the fewest significant figures overall, not necessarily decimal places.

Q: What if a number has no decimal places?

If a number has no decimal places, it implies its precision is to the nearest whole number. The result of the calculation must then also be rounded to the nearest whole number.

Q: Does this rule apply to exact numbers?

No, exact numbers (like counts or defined constants, e.g., 12 in a dozen) are considered to have infinite significant figures and do not limit the precision of the calculated result.

Q: What happens if trailing zeros are present?

Trailing zeros are significant only if the number contains a decimal point. For example, 120. has one decimal place, while 120 (without a decimal) is considered to have no decimal places when applying this rule.

Learn the specific rules for determining the correct number of significant figures when performing addition and subtraction in scientific calculations.

Have More Questions →

The Key Rule for Addition and Subtraction

When adding or subtracting measured values, the result should be rounded to the same number of decimal places as the measurement with the fewest decimal places. This rule prioritizes the precision of the measurements, ensuring that the answer doesn't imply greater accuracy than the least precise input value.

Step-by-Step Application

First, identify the number of decimal places in each of the values being added or subtracted. Then, perform the calculation. After obtaining the raw numerical answer, identify which of the original numbers had the fewest decimal places. Finally, round your calculated answer so that it has the same number of decimal places as that least precise original number.

A Practical Example

Consider adding 23.45 g (two decimal places) to 1.2 g (one decimal place). The sum is 24.65 g. According to the rule, since 1.2 g has only one decimal place (the fewest), the final answer must be rounded to one decimal place. Therefore, 24.65 g is rounded to 24.7 g. The same principle applies to subtraction.

Why This Rule is Important

This specific rule for addition and subtraction maintains consistency in reporting precision. It prevents a highly precise calculation (many decimal places) from being generated from data that includes less precise measurements. This ensures that scientific results accurately reflect the limitations of the instruments or methods used for data collection.

Frequently Asked Questions

Is this rule different from multiplication and division?

What if a number has no decimal places?

Does this rule apply to exact numbers?

What happens if trailing zeros are present?