Rounding numbers
To round to a given number of decimal places (dp) or significant figures (sf), look at the digit immediately after the place you are keeping: if it is 5 or more, round up; if it is less than 5, round down. Significant figures are counted from the first non-zero digit. For example 3.567 = 3.57 (2 dp) and 4582 = 4600 (2 sf).
Key idea
Estimate by rounding every number to 1 significant figure, then calculating. This gives a quick check on a full answer.
Worked example
Estimate 39.6 × 5.1.
Round to 1 sf: 40 × 5.
Estimate = 200.
The exact value 201.96 is close, so the answer is sensible.
Limits of accuracy
Every rounded measurement stands for a range of possible true values. It has a lower bound and an upper bound, each half a rounding unit from the stated value. A length given as 12 cm to the nearest cm could really be anything from 11.5 cm up to (but not including) 12.5 cm. These bounds matter when a measurement is used in a further calculation, for example the greatest possible area of a rectangle uses the upper bound of each side. Rounding sensibly also stops an answer from suggesting more precision than the original data allows.
Remember
- lower bound = value − ½ × (rounding unit)
- upper bound = value + ½ × (rounding unit)
- Zeros between non-zero digits are always significant.