Estimation (Cambridge (CIE) IGCSE Maths) : Revision Note

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on

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Estimation

Why do I need to estimate?

  • Estimation can be used to find approximations for difficult calculations

  • You can estimate a calculation to check your answers

    • You can identify if there is a mistake in your working out if your answer is much bigger or smaller than your estimated value

How do I estimate?

  • Round each number in the question to something sensible then perform the calculation

    • The exam question will usually tell you what to round each number to before carrying out any calculations

  • The general rule is to round numbers to 1 significant figure

    • 7.8 ➝ 8

    • 18 ➝ 20

    • 3.65 × 10-4 ➝ 4 × 10-4

    • 1080 ➝ 1000

  • In certain cases it may be more sensible (or easier) to round to something convenient

    • 16.2 ➝ 15

    • 9.1 ➝ 10

    • 1180 ➝ 1200

  • Avoid rounding values to zero

How do I know if I have underestimated or overestimated?

  • For addition a + b and multiplication a x b

a (rounded up) and/or b (rounded up)

Overestimate

a (rounded down) and/or b (rounded down)

Underestimate

  • For subtraction a - b and division a ÷ b

a (rounded up) and/or b (rounded down)

Overestimate

a (rounded down) and/or b (rounded up)

Underestimate

a (rounded up) and b (rounded up)

Not easy to tell

a (rounded down) and b (rounded down)

Not easy to tell

Examiner Tips and Tricks

  • Estimation exam questions often involve small decimals

    • Avoid rounding to 0, especially if the small decimal is the denominator of a fraction, as dividing by 0 is undefined

Worked Example

Calculate an estimate for fraction numerator 17.3 cross times 3.81 over denominator 11.5 end fraction. State, with a reason, whether the estimate is an overestimate or an underestimate.

Round each number to 1 significant figure

17.3 → 20
3.81 → 4
11.5 → 10

Perform the calculation with the rounded numbers

fraction numerator 20 cross times 4 over denominator 10 end fraction equals 80 over 10 equals 8

An estimate is 8

This is an overestimate as the numerator was rounded up and the denominator was rounded down

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Naomi C

Author: Naomi C

Expertise: Maths Content Creator

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.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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