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Cambridge IGCSE0607

Units of measure

International Mathematics 0607 Chapter Notes

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Units of measure
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Units of measure notes

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In this chapter

  1. 1Length and mass: metric units
  2. 2Area units
  3. 3Volume and capacity
  4. 4Mixed units in practical situations

1. Length and mass: metric units

Metric units of length are mm, cm, m and km. Metric units of mass are g and kg.

To change to a smaller unit, multiply. To change to a larger unit, divide.

Before you compare lengths, write them all in the same unit.

1 cm = 10 mm

1 m = 100 cm

1 km = 1000 m

1 kg = 1000 g

Examiner insight

“Those who were unable to score well were generally uncertain whether to multiply or divide their quantities by multiples of 10.”

Worked example 12 marks

Write these lengths in order of size starting with the smallest.

8000 cm 9 m 7.5 m 600 cm

  1. 1

    change to one unit: 9 m = 900 cm and 7.5 m = 750 cm [1]

  2. 2

    600 cm, 7.5 m, 9 m, 8000 cm [1]

2. Area units

Metric units of area are mm², cm², m² and km². An area unit is a length unit squared.

So the length factor is squared too. One metre is 100 cm, so 1 m² is 100 × 100 cm².

To change from m² to cm², multiply by 10 000. To change from cm² to m², divide by 10 000.

1 cm² = 100 mm²

1 m² = 10 000 cm²

1 km² = 1 000 000 m²

Examiner insight

“The most sensible unit to measure lengths in a classroom is metres and area is given by the power of 2 so the answer is m2. Some chose a volume unit or cm2.”

Worked example 11 mark

Change 4.7 m² into cm².

  1. 1

    4.7 × 10 000 = 47 000 cm² [1]

3. Volume and capacity

Metric units of volume are mm³, cm³, m³. Metric units of capacity are ml and l.

A volume unit is a length unit cubed, so the factor is cubed: 1 m³ = 100 × 100 × 100 cm³.

Volume and capacity link: 1 ml = 1 cm³, and 1 l = 1000 cm³. Also 1 m³ = 1000 l.

1 cm³ = 1 ml

1 l = 1000 ml = 1000 cm³

1 m³ = 1 000 000 cm³ = 1000 l

Examiner insight

“The starting point is the statement that 100 cm = 1 m and then this has to be cubed to turn it into the units of volume so 1 000 000 cm3 = 1 m3.” “Many thought that 5 litres = 500 ml.”

Worked example 13 marks

A box is a cuboid 20 cm by 15 cm by 10 cm. Find its volume in cm³. Then write its capacity in litres.

  1. 1

    volume = 20 × 15 × 10 [1]

  2. 2

    = 3000 cm³ [1]

  3. 3

    3000 ÷ 1000 = 3 litres [1]

4. Mixed units in practical situations

Practical questions often give measurements in mixed units, such as a length in m and a width in cm. Convert to a single unit before you calculate.

Choose the unit that suits the answer. For a capacity in litres, work in cm, find the volume in cm³, then divide by 1000.

Then look at the answer and check its size makes sense for the situation.

Examiner insight

“Candidates should be aware of the necessity to convert to a single unit when working with mixed units, as well as to make sure they present their answer in its simplest form when asked to do so.” “Most candidates recognised the need to divide the capacity by the rate of flow but the conversion of units, particularly the litres, proved too difficult for all but the best.”

Worked example 13 marks

A fish tank is a cuboid 1.2 m long, 50 cm wide and 40 cm high. Find its capacity in litres.

  1. 1

    single unit: 1.2 m = 120 cm [1]

  2. 2

    volume = 120 × 50 × 40 = 240 000 cm³ [1]

  3. 3

    240 000 ÷ 1000 = 240 litres [1]

Recap

  • To a smaller unit: multiply. To a larger unit: divide.
  • Write every measurement in the same unit before you compare or calculate.
  • 1 m = 100 cm and 1 km = 1000 m. 1 kg = 1000 g.
  • Area: square the length factor. 1 m² = 10 000 cm².
  • Volume: cube the length factor. 1 ml = 1 cm³, 1 l = 1000 cm³, 1 m³ = 1000 l.
  • Always give the unit, and check the size of the answer is sensible.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Do not use a calculator. Write 3.5 km in metres.1 mark
  2. Do not use a calculator. Write 450 g in kg.1 mark
  3. Do not use a calculator. Write these lengths in order of size, smallest first. 0.6 m  55 cm  620 mm  0.0005 km2 marks
  4. A bottle holds 0.75 l of juice. How many glasses of 150 ml can be filled from it?2 marks
  5. Do not use a calculator. Change 3 m² into cm².2 marks
  6. Change 8500 mm² into cm².2 marks
  7. A tank holds 3.2 m³ of water. Write this in litres.2 marks
  8. Do not use a calculator. A rectangle is 80 cm long and 1.5 m wide. Find its area in m².3 marks
  9. Do not use a calculator. Paper has a mass of 80 g for each square metre. One sheet of paper is a rectangle 21 cm by 30 cm. Find the mass, in kg, of a box of 5000 sheets.4 marks
  10. A rectangular floor is 3.6 m long and 2.5 m wide. It is covered with a layer of resin 4 mm thick. Resin is sold in 5-litre tins. Find the number of tins needed.5 marks

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