When a value is given to a certain degree of accuracy, it represents a range of possible values rather than a single exact number. The lower bound is the smallest possible value and the upper bound is the largest possible value.

If a number is rounded to the nearest unit, the possible error is half of that unit. The lower bound is found by subtracting half a unit and the upper bound is found by adding half a unit.

For example, if a length is given as \( 10 \) cm to the nearest centimetre, the half unit is \( 0.5 \). The true length lies between these bounds.

$$
9.5 \le x < 10.5
$$

Here, \( 9.5 \) cm is the lower bound and \( 10.5 \) cm is the upper bound.

If a mass is given as \( 4.8 \) kg to the nearest \( 0.1 \) kg, the half unit is \( 0.05 \). The bounds are found in the same way.

$$
4.75 \le x < 4.85
$$

If a value is rounded to the nearest \( 10 \), the half unit is \( 5 \). For a number given as \( 320 \) to the nearest ten, the bounds are:

$$
315 \le x < 325
$$

Upper and lower bounds are important when checking accuracy, comparing measurements and solving problems where values are approximate rather than exact.