Unit conversion | Year 9 | Ascent Library

01 / LEARN

The idea, step by step

An area contains two dimensions

A metre is 100 centimetres. A square metre is a 100 cm by 100 cm square, so it contains 10,000 square centimetres. Converting an area by the length factor alone loses one dimension. Write the square-unit conversion before multiplying or dividing.

1 m^{2} = 10000 {cm}^{2}

Volume contains three dimensions

A cubic metre is 100 cm by 100 cm by 100 cm, so it contains 1,000,000 cubic centimetres. Capacity gives another useful route: one cubic metre is 1000 litres, and one litre is 1000 millilitres. Before using a formula, put every length in the same unit.

1 m^{3} = 1000000 {cm}^{3} = 1000 L

A common trap

Using the same conversion factor for metres, square metres and cubic metres.

Instead: Use a length factor once for length, twice for area and three times for volume.

02 / WORKED EXAMPLES

See the thinking

Example 1

Convert a floor area

Convert 2.4 m² into square centimetres.

$1$ m² $= 10000$ cm².
$2.4 \times 10000 = 24000$ .

24,000 cm²

Example 2

Connect volume and capacity

Convert 0.035 m³ into litres and cubic centimetres.

In litres: $0.035 \times 1000 = 35$ L.
In cubic centimetres: $0.035 \times 1000000 = 35000$ cm³.
Check: $35$ L is $35000$ mL, and each mL is 1 cm³.

35 L and 35,000 cm³

Check your understanding

Is 1 m² equal to 100 cm² or 10,000 cm²?

Show answer

10,000 cm².

A square metre has 100 rows of 100 one-square-centimetre tiles.

03 / WORKSHEET

Your turn

6 questions · 11 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Convert 3.2 m to centimetres.
1 mark
Convert 450 cm² to square metres.
2 marks
Convert 0.006 m³ to cubic centimetres.
2 marks
Convert 7500 mL to litres.
1 mark
Convert 0.82 m² to square centimetres.
2 marks
A prism has internal dimensions 12 cm, 8 cm and 0.5 m. Find its capacity in litres.
3 marks

Read the worked solutions

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

Convert 3.2 m to centimetres.
1 mark
$3.2 \times 100 = 320$ cm.
320 cm
Convert 450 cm² to square metres.
2 marks
$450 \div 10000 = 0.045$ m².
0.045 m²
Convert 0.006 m³ to cubic centimetres.
2 marks
$0.006 \times 1000000 = 6000$ cm³.
6000 cm³
Convert 7500 mL to litres.
1 mark
$7500 \div 1000 = 7.5$ L.
7.5 L
Convert 0.82 m² to square centimetres.
2 marks
$0.82 \times 10000 = 8200$ cm².
8200 cm²
A prism has internal dimensions 12 cm, 8 cm and 0.5 m. Find its capacity in litres.
3 marks
$0.5$ m $= 50$ cm. Volume $= 12 \times 8 \times 50 = 4800$ cm³.
$4800 \div 1000 = 4.8$ L.
4.8 L

Checking saved progress…

Continue learning

Absolute, relative and percentage error

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 / South Australian Curriculum

Year 9 surface area and volume of right prisms and cylinders, capacity, absolute/relative/percentage measurement error, precision and practical measurement problems.

Official curriculum source ↗

Back to Surface area, volume and measurement