Significant figures in calculations

The problem with calculators that are too precise

A calculator often displays 8 or 10 digits after a calculation, but this number of digits has no physical meaning if the input data is less precise. The final result must be rounded to a number of significant figures consistent with the measurements used.

Rule for multiplication and division

The result retains as many significant figures as the figure with the fewest.

Example: 4.52 (3 significant figures) × 2.1 (2 significant figures) = 9.492 on the calculator, but we round to 2 significant figures -> 9.5.

Rule for addition and subtraction

The result retains as many decimal places as the figure with the fewest (not the same number of significant figures).

Example: 12.45 + 3.1 = 15.55 on the calculator; 3.1 has only one decimal place, so we round to 15.6.

Rounding correctly

We only round at the very end of the calculation, never between two intermediate steps (otherwise rounding errors accumulate). The usual rule: if the next digit is >= 5, increase the last retained digit by 1; otherwise, leave it unchanged.

Summary table

Operation	Rule applied
x, /	min of the significant figures of the operands
+, -	min of the decimal places of the operands

Common pitfall

A pupil calculates a perimeter P = 2 × (3.20 + 1.5) and retains all the digits displayed on the calculator. First, the sum must be calculated (3.20 + 1.5 = 4.7, one decimal place), then the multiplication by the exact integer 2, which does not limit the precision: P = 9.4 (consistent with the data).