From rounded measurements to intervals

A rounded measurement represents a range of possible true values. If the rounding unit is \(u\), the lower bound is half a unit below the reported value and the upper bound is half a unit above it. For positive values rounded by the usual half-up convention, include the lower endpoint and exclude the upper.

Example

A length reported as \(8.4\text{ cm}\), correct to the nearest \(0.1\text{ cm}\), satisfies \(8.35\le L<8.45\). Every value in this interval rounds to \(8.4\).

For \(3700\) correct to two significant figures, the rounding unit is \(100\), so \(3650\le x<3750\). Decide the rounding place before finding half a unit.

If a count is known to be an integer, retain only integers in the interval. A bound describes possible values; it is not a claim that the measurement error actually equals half a unit.