Error intervals

#### Tier: #Foundation #Higher

Description

When a value has been rounded, the error interval gives the range of values the original number could have been.

If a length $l$ is given as $8\text{ cm}$ (rounded to the nearest cm): $$7.5 \leq l < 8.5$$

The lower bound is found by subtracting half the degree of accuracy; the upper bound by adding half — but the upper bound uses a strict inequality ($<$) because a value of exactly 8.5 would round up to 9.

Another example — a mass $m$ rounded to 1 decimal place as $3.4\text{ kg}$: $$3.35 \leq m < 3.45$$

Error intervals are written using inequality notation, not just as a single value. The notation $\leq$ at the lower bound and $<$ at the upper bound is required — examiners penalise $\leq$ at the upper end.

Common error: forgetting the strict inequality at the upper bound, or using the wrong half-unit (e.g. using 0.5 instead of 0.05 for values rounded to 1 d.p.).

Links

Linear inequalities Bounds Rounding