Estimation

Tier: #Foundation #Higher

🔗What you need to know first

How to

Estimation means finding an approximate answer quickly by rounding values to convenient numbers — usually to 1 significant figure.

$$\frac{48.3 \times 19.7}{4.1} \approx \frac{50 \times 20}{4} = \frac{1000}{4} = 250$$

Method:

Round each value to 1 significant figure
Carry out the simplified calculation
State that the answer is an estimate

Estimation is useful for:

Checking whether a calculator answer is reasonable
Answering exam questions that say "estimate" or "use appropriate approximations"

Significant figures reminder: the first significant figure is the first non-zero digit. $0.0034$ rounded to 1 s.f. is $0.003$.

Common error: rounding to 1 decimal place rather than 1 significant figure, giving unnecessarily complex "estimates". Also: not showing the rounded values in working — the method marks require this.

Common topics that go alongside

Rounding

❓Questions to practise

Practise these questions →

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📝Past paper questions

2024 Jun 1H GCSE Q5 (1 mark)

2024 Nov 1H GCSE Q5 (2 marks)

2021 Nov 1H GCSE Q10 (2 marks)

2019 Jun 1H GCSE Q8 (3 marks)

2018 Jun 1H GCSE Q4 (1 mark)

2018 Nov 1H GCSE Q5 (1 mark)

2017 Jun 1H GCSE Q15 (1 mark)

💬What the examiners say

"Students should be aware that rounding to 1 significant figure is not always the most appropriate approach for estimation."
"As this question was testing estimation skills students were expected to round at least one value to 1 significant figure in order to get a calculation that they could work out in their heads."

⬆️How you can quickly improve

Before rounding, ask whether the result will be a calculation you can actually do mentally — for square roots, look for a nearby perfect square rather than applying one significant figure mechanically.
Write the full unrounded result before rounding, and sense-check the magnitude against what you'd expect.
State your rounded values explicitly — 'I'll round 513 to 500 and 0.81 to 0.8' — this shows the method and earns the mark.

💡Watch

🔓What this unlocks

Estimation

ℹ️Calculator tricks