Rule for significant figures in division?

The result of a division uses the same number of significant figures as the value with the fewest significant figures.

When you divide two numbers, count how many digits are meaningful in each number and use the smaller count for your answer, so you do not pretend to know more than the measurements allow. For example, if you divide eight point two by three point seven five, eight point two has two significant figures and three point seven five has three, so your final answer should keep two significant figures. Think of significant figures like how confident you are in a measurement; the least confident measurement limits how confident the final result can be. Always keep track of the original counts before rounding or you might lose accuracy.

Students often round too early and then get a wrong count of significant figures, so keep extra digits until the last step and then round to the correct number; doing calculations with full precision and rounding at the end avoids this mistake. Another common error is miscounting zeros: leading zeros do not count but zeros between nonzero digits and trailing zeros after a decimal do count, so practice counting examples to get comfortable. Sometimes numbers written as exact counts or defined constants are treated like measured values, but exact values have infinite significant figures and should not limit the result, so recognize when a number is exact versus measured.

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Significant Figures Rule for Division

1. Count significant figures in each number
2. Use the smaller count for answer
3. Do not overstate measurement precision
4. Keep original counts before rounding
5. Think of sig figs as confidence levels

Common Mistakes with Sig Fig Division

1. Rounding too early during calculations
2. Miscounting zeros in numbers
3. Treating exact values as measured

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