Chapter 2 · Measurement and Problem Solving
2.4Significant Figures in Calculations
12 min · two checks
Predict
When you multiply, which quantity decides how many significant figures the result may keep?
The idea
- Round multiplication and division by the fewest significant figures.
- Round addition and subtraction by decimal place, then handle mixed calculations.
Multiplication and division cannot create precision that the least precise factor did not have. 2.5 × 3.42 = 8.55 on a calculator, but 2.5 has two significant figures, so the reported product is 8.6. Round 5 and above up, and 4 and below down, looking at the first digit past the one you keep. Do the rounding once, at the end; keep guard digits on intermediate steps.
Addition and subtraction line up decimal places, not significant figures. 12.11 + 0.3 = 12.4, because 0.3 is known only to the tenths place. In a mixed calculation, follow the order of operations, mark how each intermediate result is limited, and apply the rule that belongs to the last operation. A common pattern is to add first (limited by decimal place) and then multiply (limited by significant figures).
Keep these
- × and ÷ : match the fewest significant figures.
- + and − : match the least precise decimal place.
- Round only the final reported value.
Worked path
A runner covers 1.25 km in 312 s. Report the average speed in m/s.
Observe
1.25 km has three significant figures. 312 s has three. Convert kilometers to meters with the exact factor 1000.