Rounding

Description

Rounding means replacing a number with a nearby value that is simpler to use. You can round to a number of decimal places (d.p.) or significant figures (s.f.).

Decimal places: count digits after the decimal point. $$3.7482 \text{ to 2 d.p.} = 3.75 \quad (\text{the third decimal is 8, so round up})$$

Significant figures: count from the first non-zero digit. $$0.004823 \text{ to 2 s.f.} = 0.0048 \quad (\text{first two sig figs are 4 and 8})$$

Rule: if the digit after your rounding point is 5 or more, round up; if less than 5, round down.

Nearest 10, 100, etc.: same principle applied to whole numbers. $$473 \text{ to the nearest 10} = 470, \quad \text{to the nearest 100} = 500$$

Common error: treating zeros after a rounded digit as insignificant — $3.50$ and $3.5$ are the same value but $3.50$ signals 2 d.p. precision.

Links

Estimation Bounds Error intervals