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.
Answer key: Converting between standard and compound units worksheet — GCSE Foundation
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- (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) 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.
- (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.
- (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.
- (b) 1.00 litres — Total volume = 350 + 650 = 1000 cm³. Since 1000 cm³ = 1 litre, the smoothie is 1.00 litre. Using only the orange juice's 650 cm³ and converting that gives 0.65 litres, forgetting the mango juice entirely. Using only the mango juice's 350 cm³ gives 0.35 litres, forgetting the orange juice. Adding both volumes correctly to get 1000 cm³ but not converting to litres leaves the answer as 1000.00, which is the volume in the wrong unit.
- (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.
- (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.
- (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.
- (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.
- (a) 200 seconds — Method: change the minutes into seconds using 1 minute = 60 seconds, then add on the loose seconds. Working: 3 × 60 = 180, and 180 + 20 = 200. Answer: 200 seconds. The distractors: 320 seconds comes from taking a minute as 100 seconds, giving 300 + 20; 180 seconds comes from converting the 3 minutes and forgetting the extra 20 seconds; 23 seconds comes from adding 3 and 20 without converting the minutes at all.
- (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.
- (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.
- (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.
- (c) 4.5 litres — Method: a litre is larger than a cm³, so changing cm³ into litres means dividing by the conversion factor 1000. Working: 4500 ÷ 1000 = 4.5. Answer: 4.5 litres. The distractors: 45 litres comes from dividing by 100; 450 litres comes from dividing by 10; 0.45 litres comes from dividing by 10 000.
- (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.
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