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R1, N13Converting units

Edexcel GCSE Maths Foundation (1MA1), Foundation tier · Ratio, proportion and rates of change

Practise Converting units. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.

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Revision notes

You must convert between metric units of length, mass and capacity, between units of time, area and volume, and between currencies or imperial units using a given rate. Conversions are often one step inside a bigger problem, so a slip here can cost you the final accuracy mark.

Grade by grade

What you need to be able to do, from the first marks up to the top grade.

  1. 2
    Convert metric units of length, mass and capacityMultiply or divide by 10, 100 or 1000, e.g. 3.4 km = 3400 m.
  2. 2
    Convert between units of timeUse 60 seconds in a minute and 60 minutes in an hour, e.g. 2.5 hours = 2 hours 30 minutes.
  3. 3
    Convert money using an exchange rateMultiply by the rate to change pounds into the other currency, and divide to change back.
  4. 3
    Read and use a conversion graphRead across and down carefully, working out the value of one small square first.
  5. 4
    Use a given metric–imperial conversionTreat it as a ratio, e.g. with 5 miles ≈ 8 km, 40 miles ≈ 64 km.
  6. 5
    Convert area and volume unitsSquare or cube the length factor, e.g. 1 m2 = 100 × 100 = 10 000 cm2.
  7. 5
    Convert between volume and capacityUse 1 cm3 = 1 ml and 1000 cm3 = 1 litre.

Notes

Metric units

  • Length: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km.
  • Mass: 1000 g = 1 kg, 1000 kg = 1 tonne.
  • Capacity: 1000 ml = 1 litre (and 100 cl = 1 litre).
  • Going to a smaller unit, multiply (you need more of them); going to a bigger unit, divide. 3.4 km = 3400 m and 250 g = 0.25 kg.

Area, volume and capacity

  • Area units are squared, so square the length factor: 1 m = 100 cm, so 1 m2 = 100 × 100 = 10 000 cm2. Also 1 cm2 = 100 mm2.
  • Volume units are cubed: 1 m3 = 100 × 100 × 100 = 1 000 000 cm3, and 1 cm3 = 1000 mm3.
  • Volume and capacity: 1 cm3 = 1 ml, 1000 cm3 = 1 litre and 1 m3 = 1000 litres.
  • Example: a box measuring 50 cm by 40 cm by 30 cm holds 60 000 cm3 = 60 litres.

Time, money and other units

  • 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day, 365 days = 1 year (366 in a leap year).
  • Time is not decimal: 0.1 hour = 6 minutes, so 2.7 hours = 2 hours 42 minutes.
  • Exchange rates: if £1 = $1.30, multiply by 1.3 to change pounds to dollars and divide by 1.3 to change back, so $91 = £70.
  • Imperial units (miles, pounds (lb), pints): the conversion is given, e.g. 5 miles ≈ 8 km. Use it like a ratio: 40 miles ≈ 64 km.
  • Conversion graphs: work out what one small square is worth. For a value off the graph, read a smaller value and multiply (only if the line goes through (0, 0)).

Cheatsheet

  • 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km
  • 1000 g = 1 kg, 1000 kg = 1 tonne
  • 1000 ml = 1 litre; 1 cm3 = 1 ml; 1000 cm3 = 1 litre
  • 1 cm2 = 100 mm2; 1 m2 = 10 000 cm2
  • 1 m3 = 1 000 000 cm3 = 1000 litres
  • To a smaller unit: multiply. To a bigger unit: divide
  • 1 hour = 60 minutes = 3600 seconds

How to answer each type of question

Convert metric units and times

1 to 2 marks2
  1. Decide if you are going to a smaller unit (multiply) or a bigger unit (divide).
  2. Use the right factor: 10, 100 or 1000 for metric units; 60 for time.
  3. For decimal hours, multiply the decimal part by 60 to get the minutes.

Example. (a) Change 4.6 kg into grams.
(b) Change 3.25 hours into hours and minutes.

Show the model answer
(a) 4.6 × 1000 = 4600 g (B1)
(b) 0.25 × 60 = 15, so 3 hours 15 minutes (B1)

Compare prices using an exchange rate

3 marks4
  1. Convert one price into the other currency: multiply to go from pounds to the other currency, divide to come back.
  2. Compare the two prices in the same currency.
  3. Write a conclusion that names the cheaper place and quotes both prices.

Example. A pair of trainers costs £72 in London.
The same trainers cost €85 in Paris.
The exchange rate is £1 = €1.16
In which city are the trainers cheaper?
You must show how you get your answer.

Show the model answer
72 × 1.16 (M1)
= €83.52 (A1)
London is cheaper, because €83.52 is less than €85 (C1)
(Or 85 ÷ 1.16 = £73.28, which is more than £72.)

Convert area units

2 marks5
  1. Square the length conversion: 1 m = 100 cm, so 1 m2 = 100 × 100 = 10 000 cm2.
  2. Multiply to go to the smaller unit; divide to go to the bigger unit.
  3. Sense check: an area in cm2 is a much bigger number than the same area in m2.

Example. The top of a table has an area of 1.8 m2.
Write this area in cm2.

Show the model answer
1.8 × 10 000, or 1.8 × 100 × 100 (M1)
= 18 000 cm2 (A1)

Find a capacity from a volume

3 marks5
  1. Change all the lengths into the same unit (usually cm).
  2. Work out the volume.
  3. Use 1000 cm3 = 1 litre (or 1 m3 = 1000 litres).

Example. A tank is a cuboid measuring 1.2 m by 80 cm by 50 cm.
How many litres of water does the tank hold when it is full?

Show the model answer
120 × 80 × 50 (M1)
= 480 000 cm3, and 480 000 ÷ 1000 (M1)
= 480 litres (A1)

Shortcuts and memory tricks

  • The prefix tells you the factor: kilo = 1000, centi = \(\frac{1}{100}\), milli = \(\frac{1}{1000}\).
  • Smaller unit, bigger number: if you change to a smaller unit and get a smaller number, you divided when you should have multiplied.
  • Picture a 1 m square: it is 100 cm by 100 cm, so its area is 10 000 cm2, not 100 cm2.
  • For rates, change one unit at a time and write the new units after every step.

Where marks are lost

  • Using 1 m2 = 100 cm2 (it is 10 000 cm2), or 1 m3 = 1000 cm3 (it is 1 000 000 cm3).
  • Treating time as decimal: 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes.
  • Multiplying by an exchange rate when you should divide: check which currency you are changing into.
  • Working out a volume with the lengths in different units.
  • Mixing up 1 litre = 1000 cm3 with 1 m3 = 1000 litres.

Exam technique

  • Write the unit with every answer, especially when the question has changed units.
  • In 'which is cheaper' questions, convert to one currency, show both amounts and write a clear conclusion.
  • Use any conversion given in the question (e.g. 1 hectare = 10 000 m2) exactly as given.
  • On a conversion graph, work out the value of one small square before you read off a value.

Sample questions

Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.

Question 1Easy2 marks
Hal says, '2.5 m2 is equal to 250 cm2, because there are 100 cm in 1 m.'
(a) Explain Hal's mistake.[1]
(b) Convert 2.5 m2 to cm2.[1]
Show the answer and mark scheme
(a) Answer: \(1 \text{ m}^2 = 100 \times 100 = 10\,000 \text{ cm}^2\), so he should multiply by 10 000, not 100.
  • C1 for explaining that 1 m2 = 10 000 cm2 (100 × 100), so the conversion factor is 10 000

Worked solution: A square of side 1 m is 100 cm by 100 cm, so its area is 10 000 cm2.

(b) Answer: 25 000 cm²
  • B1 for 25 000

Worked solution: \(2.5 \times 10\,000 = 25\,000\) cm2.

Question 2Medium4 marks
(a) Change 6.5 m3 into litres.[2]
(b) Change 81 cm2 into mm2.[2]
Show the answer and mark scheme
(a) Answer: 6500 litres
  • M1 for \(6.5 \times 1000\)
  • A1 for 6500 cao

Worked solution: \(1\text{ m}^{3} = 1000\text{ litres}\), so \(6.5 \times 1000 = 6500\) litres.

(b) Answer: 8100 mm²
  • M1 for \(81 \times 100\)
  • A1 for 8100 cao

Worked solution: \(1\text{ cm}^{2} = 10 \times 10 = 100\text{ mm}^{2}\), so \(81 \times 100 = 8100\) mm².

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