Estimation (Cambridge International IGCSE Maths)

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

Exam Hint

• 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 $\frac{17.3\times3.81}{11.5}.$ State, with a reason, whether the estimate is an overestimate or an underestimate.

Answer:

Round each number to 1 significant figure

17.3 → 20 3.81 → 4 11.5 → 10

Perform the calculation with the rounded numbers

$\frac{20\times4}{10}=\frac{80}{10}=8$

Final answer: An estimate is 8

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