Calculating with numbers: Decimal numbers
Calculation rules for significance with sum and difference
Different rules apply when adding and subtracting decimal number values for quantities. When you add two measured lengths together, you get for example \(123.4 \mathrm{\;cm} + 5.67 \mathrm{\;cm} = 129.07 \mathrm{\;cm}.\) You have to round the final answer to \(129.1 \mathrm{\;cm}.\) The precision of the first and second term is 1 and 2 decimal places, respectively. The precision cannot increase in a calculation and therefore in this case of addition the answer cannot be more accurate than \(0.1 \mathrm{\;cm}\).
The following rule applies to addition and subtraction:
The precision of the result of a calculation is equal to the lowest precision of the terms present.
In other words, the result of a calculation cannot have more digits after the decimal point than the number with the fewest digits after the decimal point.
