When should you use significant figures in calculations?

Use significant figures in hand calculations whenever measured values are involved so your answer does not imply more precision than the measurements justify, and for critical or final reports use full numeric propagation instead.

Significant figures tell you how many digits in a number are reliable based on how it was measured, so if you measured something you should not report a result with more precise digits than your least precise measurement. When you add or subtract, match the decimal place of the least precise value; when you multiply or divide, match the number of significant digits of the least precise factor. If a number comes from an exact count or a defined constant, treat it as having unlimited precision. For careful or safety-critical work, carry extra digits through calculations internally and then round only the final result, or better yet use full numeric error propagation to track uncertainties.

Students often forget the difference between the two main rules and apply the wrong one, which makes their result look either too precise or too imprecise, so remember decimal places for addition and total significant digits for multiplication and division. Another common mistake is treating zeros as always insignificant; zeros can be leading, captive, or trailing and you must decide based on decimal points whether they count. A simple tip is to write numbers in scientific notation when unsure, because it makes the number of significant digits explicit and reduces rounding errors when carrying extra digits until the final result.

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Significant Figures: When and How to Use Them

1. Use sig figs for measured values
2. Match decimal places for addition
3. Match sig figs for multiplication/division
4. Treat exact counts as unlimited precision
5. Carry extra digits internally
6. Round only the final result

Common Significant Figure Mistakes

1. Confusing addition vs multiplication rules
2. Misidentifying significant zeros
3. Rounding too early in calculations

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