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OCR MathsGeometry and measures

Units and measure conversions

Convert lengths, areas, volumes and compound units.

OCRGCSE MathsGeometry and measuresFoundation and Higher
Visual model

Changing units means multiplying by a scale factor

metrescentimetres×100\times 100area squares the scale, volume cubes it
Gold-standard guide
20 mins

What you will learn

Convert lengths, areas, volumes and compound units.
Use a clear step-by-step method for units and measure conversions.
Check your answer and avoid the most common exam mistake.
Useful before you start
Core number skillsEarlier geometry and measures skillsShowing clear working
Core knowledge

Know the rule, then use it

These are the short notes. Read each one, then check you can use it in the worked example below.

Method

Method

Length: 1 km = 1000 m = 100,000 cm

Step 1

Calculate the volume in m^3

Volume = 25 × 15 × 2 = 750 m3

Step 2

Convert m^3 to litres

1 m3 = 1000 litres

Watch out

Watch out

Students use 1 m3 = 100 litres or confuse cm3 with ml

f
Length

1m=100cm.1 m = 100 cm.

f
Area

1m2=10000cm2.1 m^{2} = 10000 cm^{2}.

f
Volume

1m3=1000000cm3.1 m^{3} = 1000000 cm^{3}.

Worked example

A swimming pool is 25 m long, 15 m wide and 2 m deep. Find its volume in litres.

1

Calculate the volume in m3: Volume = 25 × 15 × 2 = 750 m3.

2

Convert m3 to litres: 1 m3 = 1000 litres. 750 m3 = 750 × 1000 = 750,000 litres.

Final answer

750,000 litres

Question ladder

Build up to the hardest questions

Do them in order. If you miss a step, read the solution, then redo the question without looking.

Workedreasoning

A swimming pool is 25 m long, 15 m wide and 2 m deep. Find its volume in litres.

3 marks4 minsunits-and-measure-conversions-worked
Show solution
Worked solution
  1. 1.Calculate the volume in m3: Volume = 25 × 15 × 2 = 750 m3.
  2. 2.Convert m3 to litres: 1 m3 = 1000 litres. 750 m3 = 750 × 1000 = 750,000 litres.
Final answer

750,000 litres

Mark points
  • M1: calculate the volume in m3
  • M1: convert m3 to litres
  • A1: 750,000 litres
Watch out

Students use 1 m3 = 100 litres or confuse cm3 with ml. 001 m3. So 1 m3 = 1,000,000 cm3 = 1000 litres.Write the conversion chain at the top of the question.

Diagnosticrecall

Convert 5.2 km to metres.

1 mark2 minsunits-and-measure-conversions-q1
Show solution
Worked solution
  1. 1.Spot the skill: Length: 1 km = 1000 m = 100,000 cm.
  2. 2.Use the calculate the volume in m3 stage first, then convert m3 to litres.
  3. 3.Keep the final answer visible: 5200 m.
Final answer

5200 m

Mark points
  • M1: use the correct length: 1 km = 1000 m = 100,000 cm. area: 1 m2 = 10,000 cm2.volume: 1 m3 = 1,000,000 cm3 = 1000 litres. 6.
  • A1: 5200 m
Watch out

Students use 1 m3 = 100 litres or confuse cm3 with ml. 001 m3. So 1 m3 = 1,000,000 cm3 = 1000 litres.Write the conversion chain at the top of the question.

Easyprocedure

Convert 72 km/h to m/s.

2 marks3 minsunits-and-measure-conversions-q2
Show solution
Worked solution
  1. 1.Spot the skill: Length: 1 km = 1000 m = 100,000 cm.
  2. 2.Use the convert m3 to litres stage first, then calculate the volume in m3.
  3. 3.Keep the final answer visible: 20 m/s.
Final answer

20 m/s

Mark points
  • M1: use the correct length: 1 km = 1000 m = 100,000 cm. area: 1 m2 = 10,000 cm2.volume: 1 m3 = 1,000,000 cm3 = 1000 litres. 6.
  • A1: 20 m/s
Watch out

Students use 1 m3 = 100 litres or confuse cm3 with ml. 001 m3. So 1 m3 = 1,000,000 cm3 = 1000 litres.Write the conversion chain at the top of the question.

Mediumreasoning

Convert 3.5 m2 to cm2.

3 marks4 minsunits-and-measure-conversions-q3
Show solution
Worked solution
  1. 1.Spot the skill: Length: 1 km = 1000 m = 100,000 cm.
  2. 2.Use the calculate the volume in m3 stage first, then convert m3 to litres.
  3. 3.Keep the final answer visible: 35,000 cm2.
Final answer

35,000 cm2

Mark points
  • M1: use the correct length: 1 km = 1000 m = 100,000 cm. area: 1 m2 = 10,000 cm2.volume: 1 m3 = 1,000,000 cm3 = 1000 litres. 6.
  • A1: 35,000 cm2
Watch out

Students use 1 m3 = 100 litres or confuse cm3 with ml. 001 m3. So 1 m3 = 1,000,000 cm3 = 1000 litres.Write the conversion chain at the top of the question.

Hardproblem solving

A tank holds 4.5 m3. How many litres is this?

3 marks5 minsunits-and-measure-conversions-q4
Show solution
Worked solution
  1. 1.Spot the skill: Length: 1 km = 1000 m = 100,000 cm.
  2. 2.Use the convert m3 to litres stage first, then calculate the volume in m3.
  3. 3.Keep the final answer visible: 4500 litres.
Final answer

4500 litres

Mark points
  • M1: use the correct length: 1 km = 1000 m = 100,000 cm. area: 1 m2 = 10,000 cm2.volume: 1 m3 = 1,000,000 cm3 = 1000 litres. 6.
  • A1: 4500 litres
Watch out

Students use 1 m3 = 100 litres or confuse cm3 with ml. 001 m3. So 1 m3 = 1,000,000 cm3 = 1000 litres.Write the conversion chain at the top of the question.

Exam-stylemulti-step

Convert 8.5 g/cm3 to kg/m3.

4 marks6 minsunits-and-measure-conversions-q5
Show solution
Worked solution
  1. 1.Spot the skill: Length: 1 km = 1000 m = 100,000 cm.
  2. 2.Use the calculate the volume in m3 stage first, then convert m3 to litres.
  3. 3.Keep the final answer visible: 8500 kg/m3.
Final answer

8500 kg/m3

Mark points
  • M1: use the correct length: 1 km = 1000 m = 100,000 cm. area: 1 m2 = 10,000 cm2.volume: 1 m3 = 1,000,000 cm3 = 1000 litres. 6.
  • A1: 8500 kg/m3
Watch out

Students use 1 m3 = 100 litres or confuse cm3 with ml. 001 m3. So 1 m3 = 1,000,000 cm3 = 1000 litres.Write the conversion chain at the top of the question.

Grade 9 stretchproblem solving

Convert 3.2 m2 into cm2.

4 marks7 minsunits-g9
Show solution
Worked solution
  1. 1.Use 1 m = 100 cm.
  2. 2.Square the conversion factor for area.
Final answer

32,000 cm2

Mark points
  • M1: use 1002
  • A1: 32,000 cm2
Watch out

Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.

Timed checkpoint
12 mins - 9 marks

Switch between skills

Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.

1Units and measure conversions - 2 marksConvert 5.2 km to metres.Mark answer
Answer

5200 m

2Angles, lines and polygons - 2 marksThe exterior angle of a regular polygon is 24°. How many sides?Mark answer
Answer

15

3Properties of shapes - 2 marksName all 2D shapes with equal diagonals that bisect each other.Mark answer
Answer

Rectangle, square

4Perimeter, area and volume - 3 marksFind the perimeter of a rectangle with length 13 cm and width 8 cm.Mark answer
Answer

42 cm

Mastery check
  • I can explain the method for units and measure conversions.
  • I can show clear working without skipping key steps.
  • I can avoid this mistake: Students use 1 m3 = 100 litres or confuse cm3 with ml. 001 m3.So 1 m3 = 1,000,000 cm3 = 1000 litres. Write the conversion chain at the top of the question.
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Explain units and measure conversions from the beginning.Give me a hint for a units and measure conversions question.Quiz me on units and measure conversions.
Related topics
Angles, lines and polygonsProperties of shapesPerimeter, area and volume
Official exam-board sources

This guide follows the OCR GCSE Mathematics J560 specification. Practice questions are original Learnova questions shaped around official content and exam skills.

Official specification Official past papers
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