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Cambridge IGCSE0580

Units of measure

Mathematics 0580 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, mass and capacity
  2. 2Area units
  3. 3Volume and capacity
  4. 4Converting in more than one step

1. Length, mass and capacity

Metric units move in steps of 10, 100 or 1000. 1 km = 1000 m, 1 m = 100 cm and 1 cm = 10 mm. 1 kg = 1000 g. 1 l = 1000 ml.

To change to a smaller unit, multiply: there are more of them. To change to a larger unit, divide: there are fewer of them.

Check the answer. A length in cm must be a bigger number than the same length in m.

larger unit → smaller unit: multiply

smaller unit → larger unit: divide

Examiner insight

“The most common error was 5 : 2 : 1 from the incorrect conversion of 1 litre to 100 millilitres.” “In part (a) the conversion of kilometres to metres was done reasonably well although a significant number multiplied by 100, 10 or even 10 000.”

Worked example 13 marks

A ribbon is 2.4 m long. Pieces of length 30 cm are cut from it. How many whole pieces can be cut?

  1. 1

    Same units first: 2.4 m = 2.4 × 100 = 240 cm [1]

  2. 2

    240 ÷ 30 [1]

  3. 3

    = 8 pieces [1]

2. Area units

An area unit is a length unit squared. 1 cm² is 1 cm by 1 cm, which is 10 mm by 10 mm.

So the conversion factor is the length factor squared. 1 cm² = 100 mm². 1 m² = 10 000 cm². 1 km² = 1 000 000 m².

Do not use the length factor on its own. It gives an answer that is far too small or far too large.

1 cm² = 10 × 10 = 100 mm²

1 m² = 100 × 100 = 10 000 cm²

1 km² = 1000 × 1000 = 1 000 000 m²

Examiner insight

“A small majority of candidates were able to convert the area units correctly. Many however simply divided by 100 to obtain 66.1.”

Worked example 12 marks

Complete these statements.

(a) 2 kg is the same as … g.

(b) 7 cm² is the same as … mm².

  1. 1

    (a) 2 × 1000 = 2000 g [1]

  2. 2

    (b) 1 cm² = 10 × 10 = 100 mm², so 7 × 100 = 700 mm² [1]

3. Volume and capacity

A volume unit is a length unit cubed. 1 cm³ = 1000 mm³. 1 m³ = 1 000 000 cm³.

Capacity is measured in ml and l. 1 cm³ = 1 ml and 1000 cm³ = 1 l. So 1 m³ = 1000 l.

To change cm³ to litres, divide by 1000. To change litres to cm³, multiply by 1000.

1 cm³ = 1 ml

1000 cm³ = 1 l

1 m³ = 1000 l

Examiner insight

“Part (b), the conversion of cubic centimetres to litres, was less well answered as it appears that the conversion factor is not generally known.” “Less than half of the candidates knew the conversion factor to change litres into cubic centimetres.”

Worked example 11 mark

Convert 850 cm³ into litres.

  1. 1

    850 ÷ 1000 = 0.85 litres [1]

4. Converting in more than one step

Some questions need two conversions. Take them one at a time and write each line.

For a large number of cm, go through the unit between: change 2.5 km to m, then m to cm.

Show the step that converts cm³ to litres. Then give the answer in the form asked for, such as standard form.

Examiner insight

“As with the previous part, many candidates could not convert from litres to cm3 or m3 correctly.” “Few candidates showed the explicit step to convert cm3 to litres of division by 1000.”

Worked example 14 marks

Complete these statements. Give your answers in standard form.

(a) 2.5 km is the same as … cm.

(b) 30 cm³ is the same as … litres.

  1. 1

    (a) 2.5 km = 2.5 × 1000 × 100 = 250 000 cm [1]

  2. 2

    = 2.5 × 10⁵ cm [1]

  3. 3

    (b) 30 cm³ = 30 ÷ 1000 = 0.03 litres [1]

  4. 4

    = 3 × 10⁻² litres [1]

Recap

  • To a smaller unit, multiply. To a larger unit, divide.
  • 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 l = 1000 ml.
  • Area factors are the length factor squared: 1 cm² = 100 mm², 1 m² = 10 000 cm².
  • Volume factors are the length factor cubed: 1 m³ = 1 000 000 cm³.
  • 1 cm³ = 1 ml, 1000 cm³ = 1 l, 1 m³ = 1000 l.
  • Write each conversion on its own line and check the size of the answer.

End-of-chapter exercise

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

  1. Do not use a calculator. Write 4.5 kg in grams.1 mark
  2. A bottle holds 1.5 litres. Cups of 250 ml are filled from it. How many full cups can be filled?2 marks
  3. Do not use a calculator. Write 3 m² in cm².2 marks
  4. Do not use a calculator. Write 8000 mm² in cm².2 marks
  5. Do not use a calculator. A tank holds 5000 cm³ of water. Write this volume in litres.2 marks
  6. A fish tank is a cuboid 50 cm long, 40 cm wide and 30 cm high. Find the volume of water in litres when it is full.3 marks
  7. Write 2.4 m³ in litres.2 marks
  8. Do not use a calculator. A field has area 0.4 km². Write this area in m².2 marks
  9. A rectangular pool is 12 m long and 5 m wide. Water is added so that the depth of the water rises by 20 cm. A pump adds 250 litres of water each minute. How many minutes does this take?4 marks
  10. A floor is 4.5 m long and 3 m wide. It is covered with tiles that each have an area of 900 cm². The tiles are sold in packs of 12. How many packs must be bought?5 marks

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