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 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.
- 2.A cyclist travels d kilometres in t hours. Write down an expression, in terms of d and t, for the cyclist's average speed in km/h.
- 3.A force of 250 N acts on an area of 0.5 m². Using pressure = force ÷ area, work out the pressure, in pascals.
- 4.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.
- 5.A parcel has a mass of 2400 g. Given that 1 kg = 1000 g, work out the mass of the parcel in kilograms.
- 6.A section of a kitchen wall has an area of 45,000 cm². Work out the area of this section in m².
- 7.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.
- 8.The speed of a car is given by v = d ÷ t. A car travels 180 km in 3 hours. Work out the average speed of the car in km/h.
- 9.Rice costs £3.20 per kg. Work out the cost of the rice in pence per 100 g.
- 10.1 litre = 100 centilitres. Work out how many centilitres there are in 6 litres.
- 11.A bottle contains 1.5 litres of juice. Given that 1 litre = 1000 ml, work out the capacity of the bottle in millilitres.
- 12.Write 3 hours 45 minutes as a decimal number of hours.
- 13.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.
- 14.Butter costs £2.40 per kg. Work out the cost of the butter in pence per 100 g.
- 15.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.
Answer key
- (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.
- (d) d ÷ t — Average speed = distance ÷ time, so the expression is d ÷ t. Writing t ÷ d inverts the formula, giving the time per kilometre instead of the speed. Writing d × t confuses speed with the formula for distance travelled (distance = speed × time) used the wrong way round. Writing d + t treats the relationship as additive instead of using division.
- (c) 500 — Pressure = force ÷ area = 250 ÷ 0.5 = 500 pascals. Getting 125 comes from multiplying the force by the area instead of dividing (250 × 0.5 = 125). Getting 249.5 comes from subtracting the area from the force instead of dividing. Getting 50 comes from misreading the area as 5 m² instead of 0.5 m² and dividing 250 by 5.
- (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.
- (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.
- (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.
- (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.
- (d) 60 km/h — Method: use the formula v = d ÷ t with the distance and time given. Working: 180 ÷ 3 = 60 km/h. So the average speed is 60 km/h. Distractor 540 km/h comes from multiplying the distance and time instead of dividing. Distractor 90 km/h comes from dividing by 2 instead of 3. Distractor 18 km/h comes from dividing by 10 instead of 3, a decimal-point slip.
- (b) 32p — £3.20 is 320p, and 1 kg is 1000 g, which is 10 lots of 100 g. Divide the price in pence by 10: 320 ÷ 10 = 32p per 100 g. Dividing 320 by 100 instead of 10 gives 3.2p, using the wrong number of hundred-grams in a kilogram. Multiplying 320 by 10 instead of dividing gives 3200p. Forgetting to convert pounds to pence and dividing 3.20 by 10 gives 0.32, which is still in pounds rather than pence. Rice costs 32p per 100 g.
- (c) 600 centilitres — Method: changing a larger unit into a smaller one means multiplying by the conversion factor given in the question. Working: 6 × 100 = 600. Answer: 600 centilitres. The distractors: 60 centilitres comes from multiplying by 10, as if a litre held 10 centilitres; 6000 centilitres comes from multiplying by 1000, which is the number of millilitres in a litre, not centilitres; 106 centilitres comes from adding 100 and 6 instead of multiplying.
- (a) 1500 ml — Method: to change litres into millilitres, multiply by 1000. Working: 1.5 × 1000 = 1500 ml. So the bottle holds 1500 ml. Distractor 150 ml comes from multiplying by 100 instead of 1000. Distractor 15000 ml comes from multiplying by 10000, an extra zero. Distractor 1.5 ml comes from not converting the units at all.
- (d) 3.75 — 45 minutes is 45 ÷ 60 = 0.75 of an hour, so 3 hours 45 minutes = 3.75 hours. Getting 3.45 comes from writing the minutes directly after the decimal point instead of converting them to a fraction of an hour. Getting 3.67 comes from misreading 45 minutes as 40 minutes and converting 40 ÷ 60 instead. Getting 4.15 comes from rounding 45 minutes up to the next whole hour and adding the remainder as if it were more minutes past that hour.
- (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.
- (c) 24p — Method: change the price to pence, then find what one tenth of 1 kg costs, since 100 g is one tenth of 1 kg. Working: £2.40 = 240p per kg, and 240 ÷ 10 = 24p per 100 g. So the cost is 24p per 100 g. Distractor 2.4p comes from dividing by 100 instead of 10. Distractor 2400p comes from multiplying by 10 instead of dividing. Distractor 240p comes from using the price per kg without scaling it down to 100 g.
- (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.
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