Estimating answers

Foundation and Higher

The idea

To estimate, round every number to $1$ significant figure, then work it out. An estimate tells you roughly how big the answer should be.

Round each number to $1$ significant figure: $\frac{48.7 \times 3.1}{0.52} \approx \frac{50 \times 3}{0.5}$ .
Work it out: $150 \div 0.5 = 300$ .
Say whether it is an over- or underestimate when asked, by looking at how each number was rounded.

Watch out An estimate question wants the rounded working shown, not the exact calculator answer.

Worked exampleNon-calculator4 marks

Round each number to 1 significant figure to estimate each answer.

(a) Estimate the value of $612 \times 4.87$

(b) Tickets for a show cost £11.95 each. Estimate the cost of 38 tickets.

(a) Round each number to 1 significant figure. $612 \approx 600, \qquad 4.87 \approx 5$
$600 \times 5 = 3000$
(b) Round each number to 1 significant figure: $38 \approx 40$ and £11.95 £ $\approx$ 10 (to 1 significant figure, 11.95 is 10, not 12).
$40 \times 10 = 400$

Answer (a) $3000$ ; (b) £400

Question 1Non-calculator2 marks

Kate works out $4.1 \times 19.8$ and gets $811.8$ .

Use an estimate to decide whether Kate's answer is sensible. You must show how you get your answer.

Question 2Non-calculator4 marks

$\dfrac{3.94 \times 81.2}{0.487}$

(a) Work out an estimate for the value of the calculation above.

(b) Is your estimate bigger or smaller than the exact value? Give a reason.

Question 3Non-calculator4 marks

A lorry can carry at most $12$ tonnes. It needs to carry $385$ boxes, and each box has a mass of $29.7$ kg. $1$ tonne $= 1000$ kg.

(a) Estimate the total mass of the boxes, in tonnes.

(b) The driver says, "My estimate is 12 tonnes, exactly the limit, so I cannot tell whether one trip is enough." Is the driver right? Give a reason.

80 official questions in 74 papers since 2017. The latest:

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