Chemistry / Unit 1 Chem 0138 worked example, 60 to 90 seconds
Significant Figures in Multiplication and Division
The idea
When multiplying or dividing measured numbers, round the result to the same number of significant figures as the least precise number anywhere in the calculation, regardless of decimal placement.
In practice
Multiplying 0.6238 cm by 6.6 cm gives 4.11708 cm² on a calculator, but since 6.6 cm carries only two significant figures, the answer rounds to 4.1 cm². Dividing 421.23 g by 486 mL gives 0.86675... g/mL, which rounds to 0.867 g/mL to match 486's three significant figures, even though 421.23 g itself carries five.
Where people slip
This rule counts total significant figures, the opposite of the addition-and-subtraction rule, which counts decimal places — mixing the two up is the single most common significant-figures error in a multi-step calculation, and it tends to surface exactly where a calculation switches from one operation to the other.
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