Arithmetic rule
For multiplication and division, the input with the fewest significant figures controls the final answer.
Use the calculatorFor multiplication and division, count the significant figures in each measured input. The final answer should have the same number of significant figures as the input with the fewest significant figures.
The raw result is 7.75. 2.50 has 3 significant figures and 3.1 has 2, so the result is rounded to 2 significant figures: 7.8.
Before rounding the final answer, identify the significant-figures count for each input. Do not decide from decimal places here; decimal places control addition and subtraction.
4.20 has 3 significant figures and 2.0 has 2. The final product should have 2 significant figures.
0.00450 has 3 significant figures and 12.0 has 3, so the final answer should have 3 significant figures.
Keep extra digits during the raw calculation, then round once at the end. Rounding each intermediate value can move the final answer away from the best supported result.
Calculate first, identify the limiting significant-figures count, then round the final product or quotient.
Division uses the same fewest-significant-figures rule as multiplication. Count the significant figures in the numerator and denominator, then round the quotient.
10.0 has 3 significant figures and 4.0 has 2. The raw quotient 2.5 already has 2 significant figures, so report 2.5.
100. has 3 significant figures and 3.0 has 2. The final answer should have 2 significant figures.
When a rounded product or quotient ends with zeros, scientific notation can make the significant-figures count clearer than plain whole-number notation.
If the final answer needs 2 significant figures, 1.0 x 10^3 may be clearer than 1000 because the coefficient shows the precision.
Counted values and defined constants usually do not reduce the significant figures in multiplication or division. Measured values control the reported precision.
If you divide a measured total by 3 counted samples, the counted 3 is exact. The measured total controls the significant figures.
Multiplication and division often change units. Round the number by significant figures, then report the correct derived unit with the answer.
2.50 cm x 3.1 cm gives an area reported as 7.8 cm^2 because the fewest input count is 2 significant figures.
The biggest mistakes are using decimal places instead of significant figures, treating exact counted values as limiting, and dropping trailing zeros that are needed to show precision.
2.50 x 3.1 is controlled by 2 significant figures, not by one or two decimal places.
If the answer needs 3 significant figures, a value such as 1.00 x 10^2 is clearer than plain 100.
A good explanation names the rule and the limiting input. That makes the reported precision easy to verify.
The result should be reported as 7.8 because multiplication and division follow the value with the fewest significant figures.
