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Approximation and Errors: Paper 2 Multiple-Choice

Ten Paper 2 multiple-choice questions on rounding to significant figures and decimal places, the range of an actual value, percentage and relative error, and the greatest possible number of pieces. These follow the two patterns Paper 2 uses most: which rounded value is correct, and what range a measured quantity can take. Detailed solutions can be requested by email.

10 questions · about 15 minutes · answers below each question

All questions are original, written for Math and AI Academy and modelled on past-paper style. They are not reproductions of HKEAA examination questions.

Question 1 · Modelled on 2013 P2 Q4 — the digit after the cut is a 5 or a 9 in every option, so each one has to be rounded properly

$0.080 5491 =$

$0.080$ (correct to 2 significant figures).
$0.0805$ (correct to 3 decimal places).
$0.08055$ (correct to 4 significant figures).
$0.08054$ (correct to 5 decimal places).

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C. The significant figures are 8, 0, 5, 4 and the next digit is 9, so the 4 becomes 5. Option A should be $0.081$ , B should be $0.081$ and D should be $0.08055$ .

Question 2 · Modelled on 2026 P2 Q4 — the rounding carries across the decimal point

$7049.963 =$

$7050.0$ (correct to 1 decimal place).
$7049.9$ (correct to 5 significant figures).
$7049.97$ (correct to 2 decimal places).
$7000$ (correct to 3 significant figures).

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A. The second decimal place is 6, so $.9$ rounds up to $1.0$ and the carry turns $7049$ into $7050$ . B should be $7050.0$ , C should be $7049.96$ and D should be $7050$ .

Question 3 · Modelled on 2019 P2 Q6 — reversed: the rounded value is given and the range is asked

If $x = 3.47$ (correct to 3 significant figures), find the range of values of $x$ .

$3.465 < x \leq 3.475$
$3.465 \leq x < 3.475$
$3.46 \leq x < 3.48$
$3.4695 \leq x < 3.4705$

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B. The maximum absolute error is half of $0.01$ . $3.465$ rounds up to $3.47$ and is included. $3.475$ rounds up to $3.48$ and is not.

Question 4 · New sub-type, no direct past-paper model — a percentage error from one reading

The weight of a parcel is measured as $4.0 kg$ correct to the nearest $0.1 kg$ . Find the percentage error of the measurement.

$0.05%$
$0.125%$
$2.5%$
$1.25%$

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D. $\frac{0.05}{4.0} \times 100% = 1.25%$ . Option C uses $0.1 kg$ as the error instead of half of it.

Question 5 · Modelled on 2014 P2 Q11 — a perimeter instead of an area, so the error is multiplied by 4

The side of a square tile is measured as $12 cm$ correct to the nearest cm. Let $P cm$ be the actual perimeter of the tile. Find the range of values of $P$ .

$46 \leq P < 50$
$46 < P \leq 50$
$47 \leq P < 49$
$47.5 \leq P < 48.5$

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A. The side lies from $11.5 cm$ up to $12.5 cm$ , so $4 \times 11.5 \leq P < 4 \times 12.5$ . Option D treats the perimeter as if it had been measured directly.

Question 6 · Modelled on 2018 P2 Q14 — an L-shape in which every marked length pushes the area the same way

In the figure, $A BC D EF$ is a hexagon in which every two adjacent sides are perpendicular to each other, and all the measurements are correct to the nearest cm. Let $x cm^{2}$ be the actual area of the hexagon. Find the range of values of $x$ .

An L-shaped hexagon ABCDEF with all corners right angles. The bottom side is 8 cm, the left side is 6 cm, the top side is 3 cm and the short right side is 2 cm.

$27.5 \leq x < 28.5$
$26 \leq x < 30$
$18.75 \leq x < 38.75$
$21.25 \leq x < 35.25$

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D. Split the shape into a $3$ by $6$ strip and a $5$ by $2$ strip, so the area is $3 \times 6 + (8 - 3) \times 2$ . Least: $2.5 \times 5.5 + 5 \times 1.5 = 21.25$ . Upper limit: $3.5 \times 6.5 + 5 \times 2.5 = 35.25$ .

Question 7 · Modelled on 2015 P2 Q14 — litres and millilitres, with the naive answer and the least value both offered as options

The volume of water in a tank is measured as $60 L$ correct to the nearest L. All the water is poured into $n$ bottles such that the volume of water in each bottle is measured as $750 mL$ correct to the nearest $10 mL$ . Find the greatest possible value of $n$ .

$79$
$80$
$81$
$82$

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C. Use the most water and the smallest bottles: $745 n < 60500$ , so $n < 81.2 \dots$ Option B is $60000 \div 750$ . Option A is the least possible value of $n$ .

Question 8 · New sub-type, no direct past-paper model — accuracy is compared through relative error

Which of the following measurements is the most accurate?

$5 m$ , correct to the nearest m
$800 g$ , correct to the nearest $10 g$
$2.0 kg$ , correct to the nearest $0.1 kg$
$50 cm$ , correct to the nearest cm

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B. The relative errors are $\frac{1}{10}$ , $\frac{1}{160}$ , $\frac{1}{40}$ and $\frac{1}{100}$ . The smallest is $\frac{1}{160}$ .

Question 9 · New sub-type, no direct past-paper model — three statements about one reading

The length of a rod is measured as $2.4 m$ correct to the nearest $0.1 m$ . Which of the following are true?

I. The maximum absolute error of the measurement is $0.1 m$ .
II. The actual length of the rod can be $2.35 m$ .
III. The relative error of the measurement is $\frac{1}{48}$ .

I only
II only
I and III only
II and III only

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D. The maximum absolute error is $0.05 m$ , so I is false. $2.35$ rounds to $2.4$ , so II is true. $\frac{0.05}{2.4} = \frac{1}{48}$ , so III is true.

Question 10 · New sub-type, no direct past-paper model — rounding inside scientific notation

$0.000 03096 =$

$3.0 \times 1 0^{- 5}$ (correct to 2 significant figures).
$3.1 \times 1 0^{- 5}$ (correct to 2 significant figures).
$3.1 \times 1 0^{- 4}$ (correct to 2 significant figures).
$3.09 \times 1 0^{- 5}$ (correct to 3 significant figures).

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B. $0.000 03096 = 3.096 \times 1 0^{- 5}$ . To 2 significant figures this is $3.1 \times 1 0^{- 5}$ . To 3 significant figures it is $3.10 \times 1 0^{- 5}$ , not $3.09 \times 1 0^{- 5}$ .

Continue practising this topic: Try the Paper 2 Challenge MC for harder variants, or move to Paper 1 long questions — also available as Paper 1 Challenge.

Where this sits in the syllabus

Approximation and Errors is junior secondary content that the HKDSE keeps examining. From 2012 to 2026, Paper 2 carried a rounding question in most years and a range-of-values question in many, and Paper 1 Section A(1) has several times set a three-part rounding question or a claim about a total weight or capacity. The marks are reachable. They are usually lost by using the measured value where a limit is needed, or by pairing the wrong two limits.

Full coverage of this topic, and the rest of the course, is on the Mathematics page. More sets are listed on the practice index.

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