Cambridge IGCSE Maths (0580) · Non-calculator · 1.9

Estimation without a calculator

Estimating is a question type of its own, and it is also how you check every other answer on a non-calculator paper. The marks are for showing the rounded numbers you used, so write them down.

Core and Extended
Paper 1 (Core) and Paper 2 (Extended)
8 questions
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Try the questions More estimation and rounding questions

The method

Round every number to 1 significant figure, unless the question says otherwise.
Write the calculation again with the rounded numbers, before you work anything out.
If a square root or a division would be awkward, you may round to a nearby number that makes it easy (for example $63.4 \approx 64$ under a square root), but say what you used.
Dividing by a decimal such as $0.2$ or $0.05$: think "how many of these in one?" (there are $5$ lots of $0.2$ in $1$).
If asked, say whether your estimate is too big or too small: rounding the numbers you multiply up makes the estimate too big.

Worked examples

Example 1 Core non-calculator · medium

By rounding each number to 1 significant figure, estimate the value of $\dfrac{48.7 \times 3.12}{0.49}$.

$48.7 \approx 50$, $3.12 \approx 3$, $0.49 \approx 0.5$
$\dfrac{50 \times 3}{0.5} = \dfrac{150}{0.5} = 300$

Answer: $300$

Example 2 Core non-calculator · medium

Estimate the value of $\sqrt{63.4} + 2.9^2$. Show the values you use.

$63.4$ is close to the square number $64$, so $\sqrt{63.4} \approx 8$.
$2.9 \approx 3$, so $2.9^2 \approx 9$.
$8 + 9 = 17$

Answer: $17$

Common slips

Rounding to 1 decimal place instead of 1 significant figure ($0.0496$ is $0.05$ to 1 s.f.).
Working out the exact answer and then rounding it: that is not an estimate and earns no method marks.
Not showing the rounded values, so there is nothing to give a method mark for.

Practice questions

No calculator. Write down every step, then open the worked answer.

Question 1 Core non-calculator · easy

Round $0.04682$ to $2$ significant figures.

Show the worked answer

The first significant figure is the $4$; the second is the $6$.
The next digit is $8$, so round the $6$ up.

Answer: $0.047$

Question 2 Core non-calculator · easy

Estimate the value of $6.92 \times 41.3$. Show your working.

Show the worked answer

$6.92 \approx 7$ and $41.3 \approx 40$
$7 \times 40 = 280$

Answer: $280$

Question 3 Core non-calculator · medium

By rounding each number to 1 significant figure, estimate the value of $\dfrac{19.6 + 30.8}{0.24}$.

Show the worked answer

$19.6 \approx 20$, $30.8 \approx 30$, $0.24 \approx 0.2$
$\dfrac{20 + 30}{0.2} = \dfrac{50}{0.2} = 250$

Answer: $250$

Question 4 Core non-calculator · medium

By rounding each number to 1 significant figure, estimate the value of $812 \times 0.0496$.

Show the worked answer

$812 \approx 800$ and $0.0496 \approx 0.05$
$800 \times 0.05 = 40$

Answer: $40$

Question 5 Core non-calculator · medium

By rounding each number to 1 significant figure, estimate the value of $\dfrac{9.87^2}{2.03 \times 4.96}$.

Show the worked answer

$9.87 \approx 10$, $2.03 \approx 2$, $4.96 \approx 5$
$\dfrac{10^2}{2 \times 5} = \dfrac{100}{10} = 10$

Answer: $10$

Question 6 Core non-calculator · medium

A car travels $297$ km in $3.8$ hours.
Estimate its average speed. Show the values you use.

Show the worked answer

$297 \approx 300$ and $3.8 \approx 4$
$300 \div 4 = 75$

Answer: $75$ km/h

Question 7 Core non-calculator · hard

Estimate the value of $\sqrt{3.92 \times 24.6}$. Show the values you use.

Show the worked answer

$3.92 \approx 4$ and $24.6 \approx 25$, which keeps the product a square number.
$\sqrt{4 \times 25} = \sqrt{100} = 10$

Answer: $10$

Question 8 Core non-calculator · hard

Ana buys $39$ books at $11.85 each.
(a) Estimate the total cost.
(b) Is your estimate more or less than the exact cost? Give a reason.

Show the worked answer

(a) $39 \approx 40$ and $11.85 \approx 12$, so $40 \times 12 = 480$.
(b) Both numbers were rounded up, so the estimate is bigger than the exact cost.

Answer: (a) $480 (b) more than the exact cost (an overestimate), because both numbers were rounded up

Every example and question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. The syllabus is summarised in our own words: check the official 0580 syllabus.

Keep going

Estimation and Rounding questions for 0580: Core and Extended, each labelled calculator or non-calculator
Number practice for 0580, then My mistakes and a Skill Builder on what you missed
Estimation notes and the 0580 formula sheet
0580 past papers: time yourself on a specimen Paper 1 or Paper 2
All six non-calculator methods

Questions students ask

Which 0580 papers test estimation without a calculator?

Estimation is on both tiers (syllabus 1.9), so it can come up on Paper 1 (Core) and Paper 2 (Extended), the two non-calculator papers, as well as on the calculator papers.

Are these Cambridge questions?

No. The method is explained in our own words, and every example and question was written for IGCSE Math Revision and checked independently before publishing. For real papers, use the Cambridge copies linked from our 0580 past papers page.