When multiplying or dividing measured values, which rule?
When multiplying or dividing measured quantities, round the final result to the same number of significant figures as the factor with the fewest significant figures.
Think of significant figures like the number of meaningful digits in a measurement; when you multiply or divide, you cannot be more precise than your least precise number, so you match that count at the end. For example, if one measurement has three significant figures and another has five, your final answer should be rounded to three significant figures. Keep all extra digits during the calculation so rounding is done only once at the end, which avoids compounding rounding errors. If a number is an exact counted value or defined constant, it does not limit the significant figures.
A common mistake is rounding intermediate results too early, which can cause the final answer to be noticeably off, so keep extra digits during calculations and round only at the end. Another error is miscounting significant figures in numbers with zeros, such as not recognizing that leading zeros are not significant while trailing zeros in a decimal number are significant, so practice counting rules and write numbers clearly. Some students treat exact conversion factors as measured and limit precision unnecessarily, so remember that defined constants do not reduce the number of significant figures.
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Multiplication and Division Sig Fig Rule
- Match final sig figs to least precise
- Keep extra digits during calculation
- Round only once at end
- Exact values do not limit precision
Common Sig Fig Mistakes in Calculations
- Rounding intermediate results too early
- Miscounting zeros in sig figs
- Treating exact constants as measured
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