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

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?

• Sometimes, you can tell whether rounding has caused an overestimation or an underestimation

• The rules for addition and multiplication are the same

  • If both numbers are rounded up, then the answer is an overestimation

  • If both numbers are rounded down, then the answer is an underestimation

• The rules for subtract and division are the same

  • If the first number is rounded up and the second is rounded down, then the answer is an overestimation

  • If the first number is rounded down and the second is rounded up, then the answer is an underestimation

• Sometimes, you cannot tell whether the answer is an overestimation or underestimation

  • For example, $2+3=5$ is an overestimation of $2.1+2.8=4.9$

  • But $2+3=5$ is an underestimation of $2.2+2.9=5.1$

  • In both examples, the first number is rounded down to 2 and the second number is rounded up to 3

• The table below shows the different cases