Unit conversions | Year 11

01 / LEARN

The idea, step by step

Understand the idea

Metric prefixes describe powers of ten. For length, 1 m equals 100 cm and 1 km equals 1000 m. Arrange a conversion so the old unit cancels; the required unit remains.

Area has two dimensions and volume has three. One square metre contains $100 \times 100 = 10 000$ square centimetres. One cubic metre contains one million cubic centimetres.

Choose and apply a method

Identify the dimension before calculating. Square a length factor for area and cube it for volume. A length factor of 100 does not remain 100 when applied to area.

Capacity links to geometric volume: 1 mL is 1 cubic centimetre; 1 L is 1000 mL; 1 cubic metre is 1000 L. Show the unit at each stage.

1 m^{3} = 1000 L, 1 L = 1000 {cm}^{3}

A common trap

Multiplying by 100 to convert square metres to square centimetres.

Instead: Both dimensions change, so the area factor is $100^{2}$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Convert an area

Express 3.6 m $2$ in cm $2$ .

Square the length factor: $100^{2} = 10 000$ .
$3.6 \times 10 000 = 36 000$ .

36,000 cm

2

Example 2

Convert capacity

A tank has volume 0.84 m $3$ . Express it in litres and millilitres.

$0.84 \times 1000 = 840$ L.
$840 \times 1000 = 840 000$ mL.

840 L; 840,000 mL.

Check your understanding

How many litres are in 2500 cm $3$ ?

Show answer

2.5 L.

Divide by 1000 cubic centimetres per litre.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Convert 0.375 km to metres.
2 marks
Convert 4800 mm to metres.
2 marks
Convert 2.45 m $2$ to cm $2$ .
2 marks
Convert 65,000 cm $2$ to m $2$ .
2 marks
Convert 0.072 m $3$ to litres.
2 marks
Convert 450 mL to cm $3$ and litres.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Convert 0.375 km to metres.
2 marks
$0.375 \times 1000 = 375$ .
375 m.
Convert 4800 mm to metres.
2 marks
$4800 \div 1000 = 4.8$ .
4.8 m.
Convert 2.45 m $2$ to cm $2$ .
2 marks
$2.45 \times 100^{2} = 24 500$ .
24,500 cm $2$ .
Convert 65,000 cm $2$ to m $2$ .
2 marks
$65 000 \div 10 000 = 6.5$ .
6.5 m $2$ .
Convert 0.072 m $3$ to litres.
2 marks
$0.072 \times 1000 = 72$ .
72 L.
Convert 450 mL to cm $3$ and litres.
2 marks
1 mL equals 1 cm $3$ .
$450 \div 1000 = 0.45$ L.
450 cm $3$ ; 0.45 L.

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics measurement skills and applications; original explanatory lessons and papers.

Official curriculum source ↗

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