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First teaching 2023

First exams 2025

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Bounds (CIE IGCSE Maths: Core)

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Naomi C

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Naomi C

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Bounds & Error Intervals

What are bounds?

  • 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 less or equal than x less than UB
    • Note that the lower bound is included in the range of values x but the upper bound is not

How do we find the upper and lower bounds for a rounded number?

  • 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

Examiner Tip

  • 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

Worked example

The length of a road, l, is given as l equals 3.6 space 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 space less or equal than space l space less than space 3.65, although this is not asked for in this question

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Naomi C

Author: Naomi C

Expertise: Maths

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.