GCSE Unit conversion Practice Questions

Free GCSE Unit conversion practice questions with full step-by-step worked solutions. Covers metric length, mm to cm, cm to mm, m to cm. Practise exam-style problems and check your method.

metric lengthmm to cmcm to mmm to cmm to kmmm to m
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Convert 45 mm45\,\mathrm{mm} into centimetres.
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Worked solution

  1. Recall the conversion fact

    1 cm=10 mm1\,\mathrm{cm} = 10\,\mathrm{mm}

    There are 1010 millimetres in every centimetre.

  2. Decide whether to multiply or divide

    45÷1045 \div 10

    Centimetres are the larger unit, so the number of them must be smaller — divide by 1010.

  3. State the answer

    45 mm=4.5 cm45\,\mathrm{mm} = 4.5\,\mathrm{cm}

    Check by going back: 4.5×10=45 mm4.5 \times 10 = 45\,\mathrm{mm}.

Answer
4.5 cm4.5\,\mathrm{cm}
Question 2
2 markseasy
55 miles =8 km= 8\,\mathrm{km}. Convert 4040 miles into kilometres.
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Worked solution

  1. Use the given rate

    5 miles=8 km5\text{ miles} = 8\,\mathrm{km}

    Every 55 miles is worth 8 km8\,\mathrm{km}, so a mile is longer than a kilometre.

  2. Scale up to 4040 miles

    40÷5=8,8×8=6440 \div 5 = 8,\quad 8 \times 8 = 64

    4040 miles is 88 lots of 55 miles, so it is 88 lots of 8 km8\,\mathrm{km}.

  3. State the answer

    40 miles=64 km40\text{ miles} = 64\,\mathrm{km}

    The number of kilometres is bigger than the number of miles, as it must be. Check: 64÷8×5=4064 \div 8 \times 5 = 40.

Answer
64 km64\,\mathrm{km}
Question 3
2 marksintermediate
The area of a rectangle is A=lwA = lw. A rectangle has l=1.2 ml = 1.2\,\mathrm{m} and w=80 cmw = 80\,\mathrm{cm}. Work out AA in m2\mathrm{m}^2.
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Worked solution

  1. Look at the units in the formula

    l=1.2 m,w=80 cml = 1.2\,\mathrm{m},\quad w = 80\,\mathrm{cm}

    The two lengths are in different units, so the formula cannot be used yet.

  2. Choose the unit the answer needs

    answer in  m2⇒work in metres\text{answer in }\,\mathrm{m}^2 \Rightarrow \text{work in metres}

    The area is wanted in square metres, so put both lengths into metres.

  3. Convert the width

    80 cm=80÷100=0.8 m80\,\mathrm{cm} = 80 \div 100 = 0.8\,\mathrm{m}

    There are 100 cm100\,\mathrm{cm} in a metre.

  4. Substitute into the formula

    A=1.2×0.8A = 1.2 \times 0.8

    Both values are now in metres.

  5. Work out the product

    1.2×0.8=0.961.2 \times 0.8 = 0.96

    12×8=9612 \times 8 = 96, and there are two decimal places, giving 0.960.96.

  6. Check in centimetres

    120×80=9600 cm2=9600÷10000=0.96 m2120 \times 80 = 9600\,\mathrm{cm}^2 = 9600 \div 10000 = 0.96\,\mathrm{m}^2

    Working in centimetres and converting the area at the end gives the same 0.96 m20.96\,\mathrm{m}^2.

Answer
A=0.96 m2A = 0.96\,\mathrm{m}^2
Question 4
4 markshard
A worker is paid £13.50\pounds 13.50 per hour. Work out the pay for a shift lasting 77 hours 2020 minutes.
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Worked solution

  1. Write down what is given

    £13.50 per hour, 7 h 20 min\pounds 13.50\text{ per hour},\ 7\,\mathrm{h}\ 20\,\mathrm{min}

    The rate is per hour, so the time must be expressed in hours.

  2. Convert the minutes

    20 min=2060 h20\,\mathrm{min} = \frac{20}{60}\,\mathrm{h}

    There are 6060 minutes in an hour.

  3. Simplify the fraction

    2060=13\frac{20}{60} = \frac{1}{3}

    Twenty minutes is exactly one third of an hour.

  4. Write the total time

    7+13=223 hours7 + \frac{1}{3} = \frac{22}{3}\text{ hours}

    Keeping it as an exact fraction avoids rounding errors.

  5. Set up the pay

    13.50×22313.50 \times \frac{22}{3}

    Pay is the hourly rate times the number of hours.

  6. Divide by 33 first

    13.50÷3=4.5013.50 \div 3 = 4.50

    A third of an hour earns £4.50\pounds 4.50.

  7. Multiply by 2222

    4.50×22=994.50 \times 22 = 99

    The pay is £99\pounds 99.

  8. Check in minutes

    13.50÷60=0.225 per minute13.50 \div 60 = 0.225\text{ per minute}

    Route 22: the rate per minute is 22.5p22.5\mathrm{p}.

  9. Finish route 22

    440×0.225=99440 \times 0.225 = 99

    The shift is 440440 minutes, and 440×0.225=99440 \times 0.225 = 99 — the routes agree.

  10. State the answer

    Pay=£99\text{Pay} = \pounds 99

    Writing 7 h7\,\mathrm{h} 20 min20\,\mathrm{min} as "7.27.2 hours" would give £97.20\pounds 97.20 — wrong, because 0.2 h0.2\,\mathrm{h} is 1212 minutes, not 2020.

Answer
£99\pounds 99
Question 5
6 markschallenging
The mass, mm grams, of a length of wire is given by m=0.8Lm = 0.8L, where LL is the length of the wire in centimetres. A coil of this wire has mass 2 kg2\,\mathrm{kg}. Work out the length of the coil, in metres.
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Worked solution

  1. Read the formula carefully

    m=0.8Lm = 0.8L

    The formula only works if mm is in grams and LL is in centimetres.

  2. Check the units given

    m=2 kg, answer wanted in metresm = 2\,\mathrm{kg},\ \text{answer wanted in metres}

    The mass is in kilograms and the answer is wanted in metres — neither matches the formula.

  3. Convert the mass

    2 kg=2×1000=2000 g2\,\mathrm{kg} = 2 \times 1000 = 2000\,\mathrm{g}

    There are 1000 g1000\,\mathrm{g} in a kilogram, so the coil is 2000 g2000\,\mathrm{g}.

  4. Substitute into the formula

    2000=0.8L2000 = 0.8L

    Now the units on both sides agree.

  5. Rearrange for L

    L=20000.8L = \frac{2000}{0.8}

    Divide both sides by 0.80.8.

  6. Clear the decimal

    20000.8=200008\frac{2000}{0.8} = \frac{20000}{8}

    Multiplying top and bottom by 1010 makes the division exact.

  7. Work out the length in cm

    200008=2500 cm\frac{20000}{8} = 2500\,\mathrm{cm}

    The wire is 2500 cm2500\,\mathrm{cm} long.

  8. Convert to metres

    1 m=100 cm⇒2500÷100=251\,\mathrm{m} = 100\,\mathrm{cm} \Rightarrow 2500 \div 100 = 25

    The coil is 25 m25\,\mathrm{m} long.

  9. Check by substituting back

    L=2500⇒m=0.8×2500=2000 gL = 2500 \Rightarrow m = 0.8 \times 2500 = 2000\,\mathrm{g}

    2000 g2000\,\mathrm{g} is 2 kg2\,\mathrm{kg}, so the answer satisfies the original formula.

  10. Note the first classic error

    m=2⇒L=2.5 cmm = 2 \Rightarrow L = 2.5\,\mathrm{cm}

    Putting the mass in as 22 (kilograms) gives a 2.5 cm2.5\,\mathrm{cm} coil — absurd for 2 kg2\,\mathrm{kg} of wire.

  11. Note the second classic error

    L=2500 m ?L = 2500\,\mathrm{m}\ ?

    Leaving the answer as 25002500 without converting would claim a coil 2.5 km2.5\,\mathrm{km} long.

  12. Rewrite the formula for metres

    L=100x⇒m=0.8×100x=80x gL = 100x \Rightarrow m = 0.8 \times 100x = 80x\,\mathrm{g}

    If the length is xx metres, the mass in grams is 80x80x — the wire weighs 80 g80\,\mathrm{g} per metre.

  13. Convert that rule to kilograms

    m=80x1000=0.08x kgm = \frac{80x}{1000} = 0.08x\,\mathrm{kg}

    A wire xx metres long has mass 0.08x0.08x kg.

  14. Check the answer with the new rule

    0.08×25=2 kg0.08 \times 25 = 2\,\mathrm{kg}

    A 25 m25\,\mathrm{m} coil has mass 2 kg2\,\mathrm{kg} — the rebuilt formula agrees.

  15. State the answer

    L=25 mL = 25\,\mathrm{m}

    The coil of wire is 2525 metres long.

Answer
L=25 mL = 25\,\mathrm{m}

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