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 4545 mm into centimetres.
Show worked solution

Worked solution

  1. Recall the conversion fact

    1 cm=10 mm1\text{ cm} = 10\text{ mm}

    There are 10 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 10.

  3. State the answer

    45 mm=4.5 cm45\text{ mm} = 4.5\text{ cm}

    Check by going back: 4.5×10=454.5 \times 10 = 45 mm.

Answer
4.5 cm4.5\text{ cm}
Question 2
2 markseasy
55 miles =8= 8 km. Convert 4040 miles into kilometres.
Show worked solution

Worked solution

  1. Use the given rate

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

    Every 5 miles is worth 8 km, so a mile is longer than a kilometre.

  2. Scale up to 40 miles

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

    40 miles is 8 lots of 5 miles, so it is 8 lots of 8 km.

  3. State the answer

    40 miles=64 km40\text{ miles} = 64\text{ 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\text{ km}
Question 3
2 marksintermediate
The area of a rectangle is A=lwA = lw. A rectangle has l=1.2l = 1.2 m and w=80w = 80 cm. Work out AA in m2^2.
Show worked solution

Worked solution

  1. Look at the units in the formula

    l=1.2 m,w=80 cml = 1.2\text{ m},\quad w = 80\text{ 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 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\text{ cm} = 80 \div 100 = 0.8\text{ m}

    There are 100 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 0.96.

  6. Check in centimetres

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

    Working in centimetres and converting the area at the end gives the same 0.96 m2^2.

Answer
A=0.96 m2A = 0.96\text{ 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.
Show worked solution

Worked solution

  1. Write down what is given

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

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

  2. Convert the minutes

    20 min=2060 h20\text{ min} = \frac{20}{60}\text{ h}

    There are 60 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 3 first

    13.50÷3=4.5013.50 \div 3 = 4.50

    A third of an hour earns £4.50.

  7. Multiply by 22

    4.50×22=994.50 \times 22 = 99

    The pay is £99.

  8. Check in minutes

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

    Route 2: the rate per minute is 22.5p.

  9. Finish route 2

    440×0.225=99440 \times 0.225 = 99

    The shift is 440 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 h 20 min as "7.2 hours" would give £97.20 — wrong, because 0.2 h is 12 minutes, not 20.

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 22 kg. Work out the length of the coil, in metres.
Show worked solution

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\text{ 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\text{ kg} = 2 \times 1000 = 2000\text{ g}

    There are 1000 g in a kilogram, so the coil is 2000 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 0.8.

  6. Clear the decimal

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

    Multiplying top and bottom by 10 makes the division exact.

  7. Work out the length in cm

    200008=2500 cm\frac{20000}{8} = 2500\text{ cm}

    The wire is 2500 cm long.

  8. Convert to metres

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

    The coil is 25 m long.

  9. Check by substituting back

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

    2000 g is 2 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\text{ cm}

    Putting the mass in as 2 (kilograms) gives a 2.5 cm coil — absurd for 2 kg of wire.

  11. Note the second classic error

    L=2500 m ?L = 2500\text{ m}\ ?

    Leaving the answer as 2500 without converting would claim a coil 2.5 km long.

  12. Rewrite the formula for metres

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

    If the length is xx metres, the mass in grams is 80x80x — the wire weighs 80 g per metre.

  13. Convert that rule to kilograms

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

    A 25 m coil has mass 2 kg — the rebuilt formula agrees.

  15. State the answer

    L=25 mL = 25\text{ m}

    The coil of wire is 25 metres long.

Answer
L=25 mL = 25\text{ m}

Unlock 65 more Unit conversion questions

Create a free account to work through every GCSE Unit conversion question with instant step-by-step worked solutions, progress tracking and interactive lessons.

  • Full worked solutions for every question
  • Interactive lessons and instant feedback
  • Track your mastery across every topic
Create a Free Account

No card required · Free forever

More Unit conversion practice

Hard QuestionsWorked Solutions

Related Ratio & Proportion topics

Algebraic proportionCompound measuresDirect and inverse proportionDividing in a ratioRatios, fractions and linear functionsInstantaneous rate of change