Printable · GCSE Foundation · ages 14-16
Converting between standard and compound units worksheet — GCSE Foundation
Fifteen questions on "converting between standard and compound units" — DfE statement R1. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
Converting between standard and compound units worksheet — GCSE Foundation
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- 1.A cyclist rides at a steady speed of 20 mph. Given that 1 mile ≈ 1.6 km, work out the cyclist's speed in km/h.
- 2.A glass holds 250 ml of squash. Work out how many of these glasses are needed to fill a 1 litre bottle.
- 3.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.
- 4.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.
- 5.A runner's speed is 8 m/s. Given that there are 3600 seconds in an hour and 1000 metres in a kilometre, work out the runner's speed in km/h.
- 6.A section of a kitchen wall has an area of 45,000 cm². Work out the area of this section in m².
- 7.Given that 1 mile ≈ 1.6 km, work out a speed of 55 mph in km/h.
- 8.The density of a type of solid plastic is 0.9 g/cm³. Work out the mass of 0.5 m³ of the plastic, in kilograms.
- 9.A film runs for 2.25 hours. Work out the length of the film in minutes.
- 10.A parcel has a mass of 2400 g. Given that 1 kg = 1000 g, work out the mass of the parcel in kilograms.
- 11.A jug holds 2 litres. Given that 1 litre = 1000 cm³, work out the capacity of the jug in cm³.
- 12.1 metre = 100 cm. Work out how many square centimetres there are in 1 square metre.
- 13.A tap fills a tank at a rate of 15 litres per minute. Given that 1 litre = 1000 cm³, work out the rate at which the tank fills in cm³ per second.
- 14.A force of 20 N acts on an area of 4 m². Using pressure = force ÷ area, work out the pressure, in pascals.
- 15.A pump fills a paddling pool at a rate of 130 litres per hour. Work out the rate in litres per minute, to 2 decimal places.
Answer key
- (c) 32 km/h — Method: to change mph into km/h, multiply by the number of kilometres in a mile. Working: 20 × 1.6 = 32 km/h. So the cyclist's speed is 32 km/h. Distractor 12.5 km/h comes from dividing by 1.6 instead of multiplying. Distractor 21.6 km/h comes from adding 1.6 instead of multiplying by it. Distractor 20 km/h comes from not converting the units at all.
- (a) 4 — Method: put both amounts into the same unit, then divide the bottle by the glass. Working: 1 litre = 1000 ml, and 1000 ÷ 250 = 4. Answer: 4. The distractors: 0.25 comes from dividing the glass by the bottle, 250 ÷ 1000, the division the wrong way round; 40 comes from taking 1 litre as 10 000 ml; 1250 comes from adding 1000 and 250 instead of dividing.
- (c) 7800 kg/m³ — Method: build the conversion factor from the two unit changes separately — one for the mass, one for the volume. Working: 1 kg = 1000 g, so the mass figure is divided by 1000; 1 m = 100 cm, so 1 m³ = 100 × 100 × 100 = 1000000 cm³ and the volume figure is multiplied by 1000000. The density figure is therefore multiplied by 1000000 ÷ 1000 = 1000, giving 7.8 × 1000 = 7800. So the density of the metal is 7800 kg/m³. Distractor 780 kg/m³ comes from multiplying by 100 instead of 1000. Distractor 78000 kg/m³ comes from multiplying by 10000, an extra zero. Distractor 7.8 kg/m³ comes from not converting the units at all.
- (b) 6 litres — Method: find the volume of the cuboid in cm³, then change cm³ into litres using 1 litre = 1000 cm³. Working: 30 × 20 × 10 = 6000 cm³, and 6000 ÷ 1000 = 6. Answer: 6 litres. The distractors: 60 litres comes from using 1 litre = 100 cm³; 600 litres comes from using 1 litre = 10 cm³; 0.6 litres comes from using 1 litre = 10 000 cm³.
- (a) 28.8 km/h — Method: first change metres per second into metres per hour, then change metres into kilometres. Working: 8 × 3600 = 28800 metres per hour, then 28800 ÷ 1000 = 28.8 km/h. So the runner's speed is 28.8 km/h. Distractor 28800 km/h comes from stopping after the first step and forgetting to change metres into kilometres. Distractor 2.22 km/h comes from dividing by 3600 instead of multiplying, then multiplying by 1000. Distractor 2.88 km/h comes from using 360 instead of 3600 seconds in an hour, missing a zero.
- (d) 4.50 m² — 1 m² = 100 cm × 100 cm = 10,000 cm², so to convert cm² to m² you divide by 10,000: 45,000 ÷ 10,000 = 4.50 m². Dividing by 100 instead of 10,000, treating area like a length conversion, gives 45,000 ÷ 100 = 450.00 m², a common mistake since 1 m = 100 cm. Multiplying by 100 instead of dividing gives 45,000 × 100 = 4500000.00 m², using the conversion factor the wrong way round entirely. Dividing by 100,000 instead of 10,000 gives 0.45 m², an extra factor of 10 too far.
- (c) 88 km/h — Multiply the speed in mph by the conversion factor: 55 × 1.6 = 88 km/h. Dividing by 1.6 instead of multiplying gives 55 ÷ 1.6 ≈ 34.38 km/h, going the wrong way between the units. Adding the conversion factor instead of multiplying gives 55 + 1.6 = 56.6 km/h, treating the factor as an amount rather than a multiplier. Multiplying by 0.6 instead of 1.6 gives 55 × 0.6 = 33 km/h, using only part of the conversion factor. 55 mph is equal to 88 km/h.
- (b) 450.00 kg — 1 m³ = 100 × 100 × 100 = 1,000,000 cm³, so 0.5 m³ = 500,000 cm³. Mass = density × volume = 0.9 × 500,000 = 450,000 g. Converting to kilograms by dividing by 1000 gives 450,000 ÷ 1000 = 450.00 kg. Skipping the m³-to-cm³ conversion and multiplying 0.9 × 0.5 = 0.45 treats the volume as if it were already 0.5 cm³, giving 0.45 kg. Finding the mass correctly in grams, 450,000 g, but not converting to kilograms leaves 450000.00 kg, out by a factor of 1000. Using the area conversion factor of 10,000, as if converting m² to cm², instead of the volume factor of 1,000,000 gives 0.5 × 10,000 = 5,000 'cm³', and a mass of 0.9 × 5,000 = 4,500 g, which is 4.50 kg.
- (a) 135 minutes — Method: to change hours into minutes, multiply by 60. Working: 2.25 × 60 = 135 minutes. So the film runs for 135 minutes. Distractor 145 minutes comes from reading the '.25' as 25 minutes instead of a quarter of an hour, giving 2 hours 25 minutes. Distractor 225 minutes comes from multiplying by 100 instead of 60. Distractor 150 minutes comes from rounding 2.25 hours to 2.5 hours before converting.
- (a) 2.4 kg — Method: to change grams into kilograms, divide by 1000. Working: 2400 ÷ 1000 = 2.4 kg. So the parcel has a mass of 2.4 kg. Distractor 24 kg comes from dividing by 100 instead of 1000. Distractor 0.24 kg comes from dividing by 10000, an extra zero. Distractor 240 kg comes from dividing by 10 instead of 1000.
- (b) 2000 cm³ — Method: a cm³ is smaller than a litre, so changing litres into cm³ means multiplying by the conversion factor 1000. Working: 2 × 1000 = 2000. Answer: 2000 cm³. The distractors: 200 cm³ comes from multiplying by 100 instead of 1000; 20 cm³ comes from multiplying by 10; 20000 cm³ comes from multiplying by 10 000.
- (b) 10000 cm² — Method: an area conversion factor is the square of the length conversion factor, because both sides of the square are scaled. Working: a square metre is a square of side 100 cm, so its area is 100 × 100 = 10000 cm². Answer: 10000 cm². The distractors: 100 cm² comes from using the length factor without squaring it; 200 cm² comes from doubling the length factor instead of squaring it; 1000000 cm² comes from cubing the factor, which is the conversion for a volume, not an area.
- (d) 250 cm³/s — Method: first change litres per minute into cm³ per minute, then change per minute into per second. Working: 15 × 1000 = 15000 cm³ per minute, then 15000 ÷ 60 = 250 cm³ per second. So the tank fills at 250 cm³ per second. Distractor 15000 cm³/s comes from stopping after the first step and forgetting to change minutes into seconds. Distractor 900000 cm³/s comes from multiplying by 60 instead of dividing. Distractor 2500 cm³/s comes from dividing by 6 instead of 60.
- (a) 5 — Pressure = force ÷ area = 20 ÷ 4 = 5 pascals. Getting 80 comes from multiplying the force and area instead of dividing. Getting 16 comes from subtracting the area from the force (20 − 4 = 16) instead of dividing. Getting 24 comes from adding the force and area (20 + 4 = 24) instead of dividing.
- (a) 2.17 litres per minute — There are 60 minutes in an hour, so to convert litres per hour to litres per minute you divide by 60: 130 ÷ 60 = 2.1666..., which rounds to 2.17 litres per minute. Multiplying by 60 instead of dividing gives 130 × 60 = 7800.00 litres per minute, using the conversion factor the wrong way round. Leaving the rate unchanged, 130.00, ignores that 'per hour' and 'per minute' are different units. Dividing by 50 instead of 60, misremembering the number of minutes in an hour, gives 130 ÷ 50 = 2.60 litres per minute.
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