How many significant figures should I report in lab?

Use the instrument’s precision and any propagated uncertainties to determine the appropriate number of significant figures for reported values.

Think about precision like how many digits your tool can reliably show; if a ruler measures to the nearest millimeter, report to the last millimeter digit and one uncertain digit beyond if you estimate it, but do not add extra digits your tool cannot justify. When you combine measurements in calculations, small uncertainties can grow, so carry extra digits during calculation and round only at the end based on the highest uncertainty. Significant figures are a quick way to show precision for simple multiplication or division, while addition or subtraction requires matching decimal places to the least precise measurement. If your lab gives uncertainties from calibration or statistical analysis, use those to decide how many digits are meaningful rather than relying solely on raw instrument resolution.

A common mistake is keeping too many digits because calculators show long numbers, which makes results seem more precise than they are, so round to the correct significant figure after using uncertainties to guide you. Another frequent error is applying multiplication rules to addition problems and vice versa, which leads to incorrect rounding, so remember multiplication and division use significant figure counts and addition and subtraction use decimal places. Students also often ignore propagated uncertainties from intermediate steps, so carry extra digits while calculating and then round the final answer according to the combined uncertainty.

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Choosing Significant Figures in Lab Reports

1. Use instrument precision.
2. Report last reliable digit.
3. Estimate one uncertain digit.
4. Carry extra digits during calculations.
5. Round final result based on uncertainty.
6. Use sig figs for multiply/divide.
7. Match decimals for add/subtract.

Common Significant Figure Mistakes

1. Keeping too many digits
2. Using wrong rounding rule
3. Ignoring propagated uncertainties

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