AQA GCSE Maths · 3.1.3

Measures and accuracy

50 maths questions with worked answers with answers for 3.1.3 Measures and accuracy in AQA GCSE Maths (spec 8300). Practise with flashcards, a topic quiz, a random quiz across the course, 5 crosswords, or read every question and answer below. Not official AQA material.

All 50 questions and answers

Question 1 · Length · N13
Convert 3.6 km to metres.
Answer:
1 km = 1,000 m.
3.6 × 1,000 = 3,600 m.
Question 2 · Length · N13
Convert 480 cm to metres.
Answer:
100 cm = 1 m.
480 ÷ 100 = 4.8 m.
Question 3 · Length · N13
Convert 2.35 m to millimetres.
Answer:
1 m = 1,000 mm.
2.35 × 1,000 = 2,350 mm.
Question 4 · Mass · N13
Convert 2.75 kg to grams.
Answer:
1 kg = 1,000 g.
2.75 × 1,000 = 2,750 g.
Question 5 · Mass · N13
Convert 640 mg to grams.
Answer:
1,000 mg = 1 g.
640 ÷ 1,000 = 0.64 g.
Question 6 · Capacity · N13
Convert 1.8 litres to millilitres.
Answer:
1 litre = 1,000 ml.
1.8 × 1,000 = 1,800 ml.
Question 7 · Capacity · N13
Convert 750 ml to litres.
Answer:
1,000 ml = 1 litre.
750 ÷ 1,000 = 0.75 litres.
Question 8 · Area units · N13
Convert 3 m² to cm².
Answer:
1 m = 100 cm, so 1 m² = 100² = 10,000 cm².
3 × 10,000 = 30,000 cm².
Question 9 · Area units · N13
Convert 45,000 mm² to cm².
Answer:
1 cm = 10 mm, so 1 cm² = 100 mm².
45,000 ÷ 100 = 450 cm².
Question 10 · Volume units · N13
Convert 2 m³ to cm³.
Answer:
1 m = 100 cm, so 1 m³ = 100³ = 1,000,000 cm³.
2 m³ = 2,000,000 cm³.
Question 11 · Volume units · N13
How many cubic centimetres are in 1 litre?
Answer:
1 litre = 1,000 ml and 1 ml = 1 cm³.
Therefore 1 litre = 1,000 cm³.
Question 12 · Time · N13
Convert 2 hours 35 minutes to minutes.
Answer:
2 hours = 2 × 60 = 120 minutes.
120 + 35 = 155 minutes.
Question 13 · Time · N13
Convert 240 seconds to minutes.
Answer:
1 minute = 60 seconds.
240 ÷ 60 = 4 minutes.
Question 14 · Money · N13
Convert £3.65 to pence.
Answer:
£1 = 100 pence.
3.65 × 100 = 365 pence.
Question 15 · Rates · N13
A cyclist travels 45 km in 3 hours. Find the mean speed.
Answer:
Mean speed = distance ÷ time.
45 ÷ 3 = 15 km/h.
Question 16 · Rates · N13
A worker earns £72 for 8 hours. Find the hourly rate.
Answer:
Hourly rate = total pay ÷ hours.
£72 ÷ 8 = £9 per hour.
Question 17 · Rounding · N15
Round 7.483 to 1 decimal place.
Answer:
The second decimal digit is 8, so round the first decimal digit up.
7.483 rounds to 7.5.
Question 18 · Rounding · N15
Round 0.06749 to 2 significant figures.
Answer:
The first two significant digits are 6 and 7; the next digit is 4.
Keep the 7: 0.067.
Question 19 · Rounding · N15
Round 48,763 to the nearest hundred.
Answer:
The tens digit is 6, so round the hundreds digit up.
48,763 rounds to 48,800.
Question 20 · Rounding · N15
Round 9.995 to 2 decimal places.
Answer:
The third decimal digit is 5, so round up to the next hundredth.
9.995 rounds to 10.00.
Question 21 · Rounding · N15
Round 0.004876 to 3 significant figures.
Answer:
The first three significant digits are 4, 8 and 7; the next digit is 6.
Round the 7 up: 0.00488.
Question 22 · Rounding · N15
Round 65,500 to 2 significant figures.
Answer:
The first two significant digits are 6 and 5; the next digit is 5.
Round up: 66,000.
Question 23 · Rounding · N15
Round 12.349 to 2 decimal places.
Answer:
The third decimal digit is 9, so round up the second decimal digit.
12.349 rounds to 12.35.
Question 24 · Estimation · N14
Estimate 19.8 × 4.9 by rounding each number to 1 significant figure.
Answer:
19.8 rounds to 20 and 4.9 rounds to 5.
Estimated product = 20 × 5 = 100.
Question 25 · Estimation · N14
Estimate 61.2 ÷ 2.9 by rounding each number to 1 significant figure.
Answer:
61.2 rounds to 60 and 2.9 rounds to 3.
Estimated quotient = 60 ÷ 3 = 20.
Question 26 · Estimation · N14
Estimate (39.8 + 61.1) ÷ 5.1 using 1 significant figure for each number.
Answer:
Round to 1 significant figure: 39.8 ≈ 40, 61.1 ≈ 60 and 5.1 ≈ 5.
(40 + 60) ÷ 5 = 20.
Question 27 · Estimation · N14
Is 2,300 a reasonable answer to 4.1 × 5.9? Explain.
Answer:
Round to 1 significant figure: 4.1 ≈ 4 and 5.9 ≈ 6.
4 × 6 = 24, so 2,300 is far too large.
Question 28 · Estimation · N14
A bill is £19.80, £9.90 and £5.10. Estimate the total to the nearest pound for each.
Answer:
To the nearest pound: £19.80 ≈ £20, £9.90 ≈ £10 and £5.10 ≈ £5.
Estimated total = £20 + £10 + £5 = £35.
Question 29 · Accuracy · N15
A length is 8 cm to the nearest centimetre. Give its error interval.
Answer:
Half the rounding unit is 0.5 cm.
8 − 0.5 ≤ length < 8 + 0.5.
7.5 cm ≤ length < 8.5 cm.
Question 30 · Accuracy · N15
A mass is 4.2 kg to the nearest 0.1 kg. Give its error interval.
Answer:
Half the rounding unit is 0.05 kg.
4.2 − 0.05 ≤ mass < 4.2 + 0.05.
4.15 kg ≤ mass < 4.25 kg.
Question 31 · Accuracy · N15
A time is 120 seconds to the nearest 10 seconds. Give its error interval.
Answer:
Half of 10 seconds is 5 seconds.
120 − 5 ≤ time < 120 + 5.
115 s ≤ time < 125 s.
Question 32 · Accuracy · N15
A positive length is truncated to 3.7 cm to 1 decimal place. Give its error interval.
Answer:
Truncating to 1 decimal place removes later digits.
Values from 3.7 up to but excluding 3.8 truncate to 3.7.
3.7 cm ≤ length < 3.8 cm.
Question 33 · Accuracy · N16 · Higher only
A length is 6.4 m to the nearest 0.1 m. State its lower bound.
Answer:
Half of 0.1 m is 0.05 m.
Lower bound = 6.4 − 0.05 = 6.35 m.
Question 34 · Accuracy · N16 · Higher only
A mass is 9 kg to the nearest kilogram. State its upper bound.
Answer:
Half of 1 kg is 0.5 kg.
Upper bound = 9 + 0.5 = 9.5 kg; the true mass is below it.
Question 35 · Bounds · N16 · Higher only
A rectangle has sides 5 cm and 8 cm, each rounded to the nearest cm. Find the lower bound for its area.
Answer:
Lower bounds of the positive sides are 4.5 cm and 7.5 cm.
Lower area bound = 4.5 × 7.5 = 33.75 cm².
Question 36 · Bounds · N16 · Higher only
A rectangle has sides 5 cm and 8 cm, each rounded to the nearest cm. Find the upper bound for its area.
Answer:
Upper bounds of the positive sides are 5.5 cm and 8.5 cm.
Upper area bound = 5.5 × 8.5 = 46.75 cm²; the true area is below it.
Question 37 · Bounds · N16 · Higher only
A distance is 120 m and a time is 20 s, both to the nearest unit. Find the upper bound for speed.
Answer:
Use the upper distance bound 120.5 m and lower time bound 19.5 s.
Upper speed bound = 120.519.5 = 24139 m/s ≈ 6.18 m/s.
Question 38 · Bounds · N16 · Higher only
A length is 12.0 cm to the nearest 0.1 cm. State the interval for twice its length.
Answer:
The length satisfies 11.95 cm ≤ length < 12.05 cm.
Double both bounds: 23.9 cm ≤ twice the length < 24.1 cm.
Question 39 · Significant figures · N15
How many significant figures are in 0.03040?
Answer:
Leading zeros do not count; zeros between or after significant digits do.
The significant digits are 3, 0, 4, 0: four figures.
Question 40 · Significant figures · N15
Give 0.00994 to 1 significant figure.
Answer:
The first significant digit is 9 and the next is 9, so round up.
0.00994 rounds to 0.01.
Question 41 · Context · N15
A coach seats 48 people. How many coaches are needed for 100 people?
Answer:
100 ÷ 48 is just over 2.
Two coaches hold only 96 people, so 3 coaches are needed.
Question 42 · Context · N13
A train leaves at 09:45 and arrives at 11:20. How long is the journey?
Answer:
09:45 to 10:45 is 1 hour; 10:45 to 11:20 is 35 minutes.
Total = 1 hour 35 minutes.
Question 43 · Context · N13
A packet costs £1.35. Find the cost of 4 packets.
Answer:
Multiply the cost of one packet by 4.
£1.35 × 4 = £5.40.
Question 44 · Context · N13
A parcel has a mass of 1.2 kg. What is the mass of 5 parcels in grams?
Answer:
5 × 1.2 kg = 6 kg.
6 × 1,000 = 6,000 g.
Question 45 · Accuracy · N14
Estimate the area of a 9.8 cm by 3.1 cm rectangle using 1 significant figure.
Answer:
9.8 cm ≈ 10 cm and 3.1 cm ≈ 3 cm.
Estimated area = 10 × 3 = 30 cm².
Question 46 · Accuracy · N15
Why keep extra digits until the final step?
Answer:
Rounding an intermediate result changes the number used in later calculations.
Keep extra digits and round at the end to reduce accumulated rounding error.
Question 47 · Accuracy · N15
A number rounded to the nearest 10 is 70. Can its true value be 75?
Answer:
Values that round to 70 satisfy 65 ≤ value < 75.
75 rounds to 80, so it cannot be the true value.
Question 48 · Units · N13
Convert 0.45 m² to cm².
Answer:
1 m² = 10,000 cm².
0.45 × 10,000 = 4,500 cm².
Question 49 · Units · N13
Given 1 mile = 1.6 km, convert 5 miles to km.
Answer:
Multiply the number of miles by 1.6.
5 × 1.6 = 8 km.
Question 50 · Units · N13
A 750 ml bottle is filled three times. How many litres is that?
Answer:
750 ml × 3 = 2,250 ml.
2,250 ÷ 1,000 = 2.25 litres.

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