IGCSE · Practice questions · Rounding and estimation

One digit decides, zeros hold the place.

Six original Cambridge-style questions on rounding, estimating and choosing a sensible accuracy.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Find the last digit kept, look at the next one.

Deciding digit: 5 or more rounds up; 4 or less does not.
Significant figures start at the first non-zero digit.
Place holders: fill with zeros in whole numbers; keep trailing zeros in decimals (8.00).
Estimate: every number to 1 s.f., show the rounded numbers, then calculate.
Context: round up or down so the answer makes sense; money to 2 d.p.

Recall

[3 marks]

Write (a) 5764 correct to the nearest hundred (b) 0.073 586 correct to 3 significant figures (c) 19.996 correct to 2 decimal places.

(a) 5800 ✓
(b) 0.0736 ✓
(c) 20.00 ✓

Recall

[2 marks]

Write (a) 0.000 806 1 correct to 2 significant figures (b) 2 049 600 correct to 3 significant figures.

(a) 0.000 81 ✓
(b) 2 050 000 ✓

Calculation

[2 marks]

By rounding each number to 1 significant figure, estimate the value of $\dfrac{19.6 \times 3.08}{0.51}$. Show your working.

$\dfrac{20 \times 3}{0.5}$ ✓
$= \dfrac{60}{0.5} = 120$ ✓

Calculation

[3 marks]

(a) Estimate $\sqrt{98.6} \times 4.92$, showing your working.

(b) Use your calculator to find the exact value, correct to 3 significant figures.

(a) $\sqrt{100} \times 5 = 50$ ✓
(b) $48.854\dots = 48.9$ ✓
(c) Overestimate: both 98.6 and 4.92 were rounded UP. ✓

Analysis

[2 marks]

Three friends share a restaurant bill of $86.35 equally.

(a) Work out each share, correct to the nearest cent. (b) Explain why each friend should actually pay $28.79.

(a) $86.35 \div 3 = 28.783\dots = \$28.78$ ✓
(b) $3 \times 28.78 = 86.34$, which is 1 cent short of the bill, so each must pay $28.79 to cover it. ✓

Analysis

[4 marks]

A room has 47.8 m² of wall to paint, and it needs two coats. One litre of paint covers 11.5 m². Paint is sold in 2.5-litre tins.

(a) By rounding each number to 1 significant figure, estimate the number of litres needed.

(b) Calculate the number of tins that must be bought.

(a) $\dfrac{2 \times 50}{10} = 10$ litres ✓
(b) Litres: $2 \times 47.8 \div 11.5 = 8.313\dots$ ✓
Tins: $8.313\dots \div 2.5 = 3.33\dots$ ✓
3 tins would not be enough, so round up: 4 tins. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.