How do significant figures work in subtraction?

When subtracting in chemistry, you round the final answer to the same number of decimal places as the measurement with the fewest decimal places.

Imagine you have numbers like three point one four and one point two; you line up the decimals and subtract like normal, then look at how many digits are after the decimal in each original measurement and keep only that many decimal places in your answer. If one number has one decimal place and the other has two, your result must be rounded to one decimal place because that is the least precise measurement. This rule is about decimal places, not total digits, so even a large number with no decimals counts as zero decimal places and forces a whole number result. Always keep track of the original decimal places before you round, because intermediate steps can have more digits but the final answer must match the least number of decimal places.

A common mistake is treating significant figures the same for addition and subtraction as for multiplication and division, which uses total significant digits; remember subtraction uses decimal places, not significant digits, so do not count digits to the left of the decimal unless they are part of the decimal places rule. Another error is rounding too early during calculations; if you round intermediate results you can introduce big errors, so do the subtraction first and round only the final answer to the correct number of decimal places. Students also sometimes forget to align decimal points before subtracting, which leads to wrong values, so always write numbers vertically with decimals lined up before you subtract.

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Significant Figures in Subtraction

1. Line up decimal points vertically
2. Subtract normally before rounding
3. Count decimal places in originals
4. Round final answer to least decimals
5. Large whole numbers force zero decimals
6. Keep track of original decimal places

Common Mistakes with Significant Figures

1. Confusing rules for different operations
2. Rounding intermediate results too early
3. Not aligning decimal points before subtracting

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