The result of a multiplication uses the same number of significant figures as the factor with the fewest significant figures.
When you multiply numbers, you look at how many digits actually count in each number and then keep that many digits in your answer. Imagine you have one number that is only sure to two digits and another that is sure to four digits; your final product can only be trusted to two digits too, because the less precise number limits how accurate the result can be. This is like measuring with a ruler that only shows centimeters and another that shows millimeters—your final answer can only be as good as the less precise tool. When rounding, do it at the end after you have completed the calculation, not after each step, so small rounding errors do not pile up.
Common mistakes include counting zeros at the end of a number written with a decimal point or not recognizing which zeros are significant, and a quick fix is to write numbers in scientific notation so it is clear how many digits are meaningful. Another mistake is rounding intermediate results too early, and the simple solution is to keep extra digits through the calculation and round only the final answer. Some students forget to check the original numbers for implied precision, and the remedy is to always examine how the numbers were measured or written before deciding how many significant figures to report.
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Rule for Significant Figures in Multiplication
- Count significant digits in each number
- Keep final digits equal to least precise
- Think of less precise tool limiting accuracy
- Round only after completing calculation
Common Mistakes with Significant Figures
- Misidentifying which zeros are significant
- Rounding intermediate results too early
- Ignoring implied precision of original numbers
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