Bounds | CIE IGCSE Maths: Core Revision Notes 2025

Bounds & Error Intervals

Bounds are the values that a rounded number can lie between
- The smallest value that a number can take is the lower bound (LB)
- The largest value that a number must be less than is the upper bound (UB)
The bounds for a number, $x$ , can be written as $LB \leq x < UB$
- Note that the lower bound is included in the range of values $x$ but the upper bound is not

Identify the degree of accuracy to which the number has been rounded
- E.g. 24 800 has been rounded correct to the nearest 100
Divide the degree of accuracy by 2
- E.g. If an answer has been rounded to the nearest 100, half the value is 50
Add this value to the number to find the upper bound
- E.g. 24 800 + 50 = 24 850
Subtract this value from the number to find the lower bound
- E.g. 24 800 - 50 = 24 750
The error interval is the range between the upper and lower bounds
- Error interval: LB ≤ x < UB
- E.g. 24 750 ≤ 24 800 < 24 850

Read the exam question carefully to correctly identify the degree of accuracy
- It may be given as a place value, e.g. rounded to 2 s.f.
- Or it may be given as a measure, e.g. nearest metre

The length of a road, $l$ , is given as $l = 3.6 km$ , correct to 1 decimal place.

Find the lower and upper bounds for $l .$

The degree of accuracy is 1 decimal place, or 0.1 km
Divide this value by 2

0.1 ÷ 2 = 0.05

The true value could be up to 0.05 km above or below the given value

Upper bound: 3.6 + 0.05 = 3.65 km

Lower bound: 3.6 - 0.05 = 3.55 km

Upper bound: 3.65 km
Lower bound: 3.55 km

We could also write this as an error interval of $3.55 \leq l < 3.65$ , although this is not asked for in this question