The problems are on the SI units worksheet. Try them on your own first, then compare with the answers below.
Quick answer: SI units are the internationally agreed units for measurement: metre for length, kilogram for mass, second for time, ampere for current and kelvin for temperature. These worked answers correct the 20 problems of the Physics 9-10 worksheet on SI units, from base units to which result to trust: each solution shows the formula, the substitution and the final answer with its unit.
Each answer shows the formula or rule, the substitution and the final result in bold with its unit. Check your significant figures as well as your numbers, because examiners award marks for both.
Level: Physics grades 9-10 (GCSE · IGCSE · O Level · Class 9-10) · Curriculum: GCSE WS, IGCSE 1.1
Problem 1 Base units
1 and 2. Length: metre (m); mass: kilogram (kg); time: second (s); current: ampere (A); temperature: kelvin (K).
3. The kilogram contains the prefix kilo.
Problem 2 Prefix factors
1. kilo = 10³.
2. milli = 10⁻³.
3. micro = 10⁻⁶.
4. giga = 10⁹.
Problem 3 Simple conversions
1. 2.5 × 1000 = 2500 m.
2. 340 × 10⁻³ = 0.34 m.
3. 75 × 10⁻² = 0.75 m.
4. 0.8 × 1000 = 800 g.
Problem 4 Standard form
1. 4.5 × 10⁷.
2. 6.2 × 10⁻⁴.
3. 3800.
4. 0.071.
Problem 5 Counting significant figures
1. 502 has 3 s.f. (the zero is between digits).
2. 0.0405 has 3 s.f.
3. 1.050 has 4 s.f. (the trailing zero after the point counts).
4. 0.0090 has 2 s.f.
Problem 6 Rounding
1. 3.14.
2. 0.0068.
3. 25 000 (2.5 × 10⁴).
4. 9.996 rounds up to 10.0.
Problem 7 Reading a ruler
1. The smallest division is 1 mm, so the resolution is 1 mm (0.1 cm).
2. The strip ends 3 small marks after 6 cm: 6.3 cm.
3. 6.3 × 10⁻² = 0.063 m.
Problem 8 Area of a tile
1. 18.4 × 12.5 = 230 cm² (3 s.f.).
2. 1 m² = 10 000 cm², so 230 ÷ 10 000 = 0.023 m² (2.3 × 10⁻² m²).
3. Both measurements have 3 s.f.
Problem 9 Area and volume units
1. 3.2 × 10 000 = 32 000 cm² (3.2 × 10⁴ cm²).
2. 1 m³ = 10⁶ cm³, so 450 ÷ 10⁶ = 4.5 × 10⁻⁴ m³.
3. A square metre is 100 cm wide and 100 cm long, so it holds 100 × 100 = 10 000 cm². The factor 100 applies to each of the two lengths.
Problem 10 Time conversions
1. 2.4 × 3600 = 8640 s.
2. 45 × 60 + 30 = 2700 + 30 = 2730 s.
3. 0.5 × 10⁻³ = 5 × 10⁻⁴ s.
Problem 11 Averaging a pendulum
1. Sum = 14.8 + 15.2 + 15.0 + 14.9 + 15.1 = 75.0, so mean = 75.0 ÷ 5 = 15.0 s.
2. 15.0 ÷ 10 = 1.50 s per swing.
3. (15.2 − 14.8) ÷ 2 = 0.2 s.
Problem 12 Two balances
1. A: (5.31 + 5.30 + 5.32) ÷ 3 = 15.93 ÷ 3 = 5.31 g. B: (4.9 + 5.2 + 5.0 + 4.9) ÷ 4 = 20.0 ÷ 4 = 5.00 g.
2. A has a range of 0.02 g and B has 0.3 g, so balance A is more precise.
3. B’s mean equals the true value, so balance B is more accurate. A is precise but not accurate, like the second target.
Problem 13 Percentage uncertainty
1. 0.5 ÷ 25.0 × 100 = 2.0 %.
2. 0.01 ÷ 0.40 × 100 = 2.5 %.
3. The length has the smaller percentage uncertainty (2.0 % against 2.5 %).
Problem 14 Density from a block
1. V = 10.0 × 3.0 × 6.0 = 180 cm³.
2. Density = 540 ÷ 180 = 3.0 g/cm³.
3. 1 g/cm³ = 1000 kg/m³, so the density is 3000 kg/m³ (3.0 × 10³ kg/m³).
Problem 15 Thickness of a sheet
1. 2.0 ÷ 200 = 0.010 cm = 0.10 mm.
2. 0.1 ÷ 2.0 × 100 = 5 %.
3. 5 % of 0.10 mm = 0.005 mm, so 0.100 ± 0.005 mm.
4. 0.10 mm = 0.10 × 10⁻³ m = 1.0 × 10⁻⁴ m.
Problem 16 Speed and sensible rounding
1. 100.0 ÷ 12.4 = 8.0645… m/s.
2. 8.06 m/s.
3. The time has 3 s.f. and the distance has 4 s.f., so the answer is limited to 3 s.f. by the time.
Problem 17 Speed unit change
1. 90 × 1000 ÷ 3600 = 25 m/s.
2. 1.2 × 10⁻³ × 1000 = 1.2 L.
3. 20 × 3600 ÷ 1000 = 72 km/h.
Problem 18 Distance light travels in a year
1. d = 3.0 × 10⁸ × 3.2 × 10⁷ = 9.6 × 10¹⁵, so 9.6 × 10¹⁵ m.
2. Dividing by 1000 gives 9.6 × 10¹² km.
3. Both inputs have 2 s.f., so the answer has 2 s.f.
Problem 19 Spot the errors
1. The student multiplied by 1000 instead of using 10⁻³. 5.6 mm = 5.6 × 10⁻³ m = 0.0056 m.
2. Micro means 10⁻⁶, not 10⁻³. 0.75 µA = 0.75 × 10⁻⁶ A = 7.5 × 10⁻⁷ A.
3. 7.5 × 10⁻⁷ A ÷ 10⁻³ A per mA = 7.5 × 10⁻⁴ mA.
Problem 20 Which result to trust
1. G1: 37.23 ÷ 3 = 12.41 m. G2: 38.37 ÷ 3 = 12.79 m. G3: 37.2 ÷ 3 = 12.4 m.
2. The ranges are 0.02 m for G1, 0.02 m for G2 and 0.6 m for G3. G1 and G2 are equally precise and G3 is the least precise.
3. The means differ from 12.40 m by 0.01 m (G1), 0.39 m (G2) and 0.0 m (G3). G3’s mean is closest, but only by luck because its readings are widely spread. G1 is the best overall.
4. A systematic error, such as a stretched tape or a measurement started from the wrong mark, shifts all of G2’s readings the same way.
