Estimation (Cambridge (CIE) IGCSE International Maths)

Revision Note

Author

Expertise

Maths

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

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

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

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

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

Calculate an estimate for $\frac{17.3 \times 3.81}{11.5} .$ 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

$\frac{20 \times 4}{10} = \frac{80}{10} = 8$

An estimate is 8

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

the (exam) results speak for themselves:

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