All measurements are approximate. This is because measuring instruments have limited precision and it is not possible to measure a quantity exactly. When a measurement is given, the true value is assumed to lie within a small range.

If a measurement is rounded to the nearest unit, the maximum possible error is half of that unit. This means the actual value could be up to half a unit higher or half a unit lower than the stated measurement.

For example, a length measured as \( 8 \) cm to the nearest centimetre could actually be anywhere between \( 7.5 \) cm and \( 8.5 \) cm.

This can be written as an inequality.

$$
7.5 \le 8 < 8.5
$$

The same idea applies to other units. If a mass is given as \( 3.2 \) kg to the nearest \( 0.1 \) kg, the possible error is half of \( 0.1 \), which is \( 0.05 \).

The true mass lies between:

$$
3.15 \le 3.2 < 3.25
$$

Understanding that measurements have a possible error is important when checking accuracy, setting bounds and deciding whether results are sensible in context.