Round every number to 1 significant figure, then calculate quickly to get a sensible approximate answer. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
An estimate is a 1-significant-figure version of a calculation, done so you can judge a calculator answer or survive a non-calculator paper. Round every number in the question to 1 s.f., including decimals less than 1 (0.048 becomes 0.05), then compute. Write ≈ and show the rounded calculation, not just the final guess.
Saying whether you over-estimated or under-estimated needs a reason: you rounded a denominator up, so the fraction came out smaller, and so on. An estimate of 400 for a true value of 412 is healthy; 40 or 4000 means a decimal place has wandered.
Round every number to 1 significant figure, then calculate. The point of the estimate is a number you can do in your head so a calculator slip (or a non-calc product) can be sense-checked. a2+b2 estimates are 3-4-5 triangles in disguise.
Objectives
Keep the first non-zero digit and turn the rest into zeros.
Estimate 19 × 21 as 20 × 20 = 400.
Estimate 612 ÷ 28 as 600 ÷ 30 = 20.
Key points
Round any number, including decimals less than 1, to 1 significant figure.
Estimate a calculation involving ×, ÷, powers and square roots.
Use the ≈ symbol correctly and show the rounded calculation.
Say whether your estimate is an over- or under-estimate and explain why.
Worked examples
Example 1
Estimate 19 × 12 by rounding each number to 1 significant figure.
2 marks
19 rounds to 20 and 12 rounds to 10.
20 × 10 = 200.
The estimate is 200.
Answer: 200
Common slips
Slip: 21 rounds to 20 and 12 rounds to 10. That changes a number from the question, so it answers a different question.
Slip: 20 + 10 = 30. That uses addition, but this step needs multiplication.
Slip: The estimate is 204. That does not match the working above it.
Example 2
Estimate 394 ÷ 19 by rounding each number to 1 significant figure.
2 marks
394 rounds to 400 and 19 rounds to 20.
400 ÷ 20 = 20.
The estimate is 20.
Answer: 20
Common slips
Slip: 396 rounds to 400 and 19 rounds to 20. That changes a number from the question, so it answers a different question.
Slip: 400 × 20 = 8000. That uses multiplication, but this step needs division.
Slip: The estimate is 24. That does not match the working above it.
Example 3
Estimate 6.1 × 0.52 by rounding each number to 1 significant figure.
2 marks
6.1 rounds to 6 and 0.52 rounds to 0.5.
6 × 0.5 = 3.
The estimate is 3.
Answer: 3
Common slips
Slip: 8.1 rounds to 6 and 0.52 rounds to 0.5. That changes a number from the question, so it answers a different question.
Slip: 6 + 0.5 = 6.5. That uses addition, but this step needs multiplication.
Slip: The estimate is 7. That does not match the working above it.
Questions and answers
GCSE Maths estimating questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Which two consecutive whole numbers does √70 lie between?
Show answer
Answer: 8 and 9
8² = 64 and 9² = 81.
70 is between 64 and 81, so √70 is between 8 and 9.
M1 — 8² = 64 and 9² = 81.
A1 — Answer 8 and 9
Question 2 Easy2 marks
Estimate 69 × 62 by rounding each number to 1 significant figure.
Show answer
Answer: 4200
69 rounds to 70 and 62 rounds to 60.
70 × 60 = 4200.
M1 — 69 rounds to 70 and 62 rounds to 60.
A1 — Answer 4200
Question 3 Medium2 marks
Which two consecutive whole numbers does √50 lie between?
Show answer
Answer: 7 and 8
7² = 49 and 8² = 64.
50 is between 49 and 64, so √50 is between 7 and 8.
M1 — 7² = 49 and 8² = 64.
A1 — Answer 7 and 8
Question 4 Medium2 marks
Estimate 39 × 32 by rounding each number to 1 significant figure.
Show answer
Answer: 1200
39 rounds to 40 and 32 rounds to 30.
40 × 30 = 1200.
M1 — 39 rounds to 40 and 32 rounds to 30.
A1 — Answer 1200
Question 5 Hard2 marks
Which two consecutive whole numbers does √130 lie between?
Show answer
Answer: 11 and 12
11² = 121 and 12² = 144.
130 is between 121 and 144, so √130 is between 11 and 12.
M1 — 11² = 121 and 12² = 144.
A1 — Answer 11 and 12
Question 6 Hard2 marks
Estimate 89 × 82 by rounding each number to 1 significant figure.
Show answer
Answer: 7200
89 rounds to 90 and 82 rounds to 80.
90 × 80 = 7200.
M1 — 89 rounds to 90 and 82 rounds to 80.
A1 — Answer 7200
Question 7 Exam-style2 marks
Which two consecutive whole numbers does √90 lie between?
Show answer
Answer: 9 and 10
9² = 81 and 10² = 100.
90 is between 81 and 100, so √90 is between 9 and 10.
√90 lies between 9 and 10.
M1 — 9² = 81 and 10² = 100.
A1 — Answer 9 and 10
Common mistakes
Most lost marks on this topic are one slip.
Calculating the exact product and calling it an estimate.
Round first, then calculate.
Rounding 19 down to 10.
19 is closer to 20.
Forgetting that the estimate is allowed to differ from the exact value.
It should be the right size, not the exact answer.
Spot the slip
19 to one significant figure is
20
19
10
Show the slip
20 The first digit is 1, and the next digit rounds it up to 20.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the rounded calculation on its own line — the first mark is almost always for correct rounding.
Use ≈ not = once you have rounded.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.