How many decimals to report from measurements?

Use the same number of decimal places as the least precise measurement in your calculation unless you are doing a formal uncertainty propagation, in which case follow the propagation rules and report the result with the appropriate uncertainty and corresponding significant figures.

Think of each measurement like a ruler with marks: some rulers have big marks so you can only tell to the nearest whole number, and some have tiny marks so you can tell to the nearest tenth or hundredth. When you add or subtract, the answer can only be as precise as the least precise ruler, so you match the number of decimal places of the least precise measurement. When you multiply or divide, you match the number of significant figures of the least precise measurement instead of decimal places. If you want to be more rigorous, calculate the uncertainty for each number, carry those uncertainties through the math using propagation formulas, and then report the result with its uncertainty; the digits you keep should reflect that uncertainty so you are not pretending to know more than you do.

A common mistake is counting significant figures wrong, for example thinking trailing zeros without a decimal point are significant when they might not be; fix this by writing numbers in scientific notation to make significant figures clear. Another error is applying the decimal place rule to multiplication or division; remember to switch to significant figures for those operations. A third is reporting an answer with too many digits after doing an uncertainty calculation; round the final value to match the uncertainty so your result does not imply greater precision than supported.

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How Many Decimals to Report from Measurements?

1. Match least precise decimal places
2. Add/subtract use decimal places
3. Multiply/divide use significant figures
4. Calculate uncertainties for rigor
5. Report result with appropriate uncertainty

Common Significant Figures Mistakes

1. Miscounting significant figures
2. Using decimal rule for multiplication
3. Reporting too many digits after uncertainty

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