The idea, step by step
A unit tells us what one step means
Measure length with a ruler or tape and say which unit you used. A pencil might be 16 cm long, while the trip to school might be 3 km. Converting changes the number, not the actual length. Since 1 m contains 100 cm, multiply a length in metres by 100 to name it in centimetres. Divide by 100 to reverse the conversion.
Square and cubic units behave differently. A square metre contains 100 rows of 100 square centimetres, so it contains 10,000 cm². A cubic metre contains 100 layers of 100 by 100 small cubes, so it contains 1,000,000 cm³.
Precision should suit the instrument
A whole-centimetre measurement does not tell us all the millimetres. Keep extra digits while calculating, then round the final answer to a useful place. Explain your rounding if the question leaves a choice. An estimate such as about 2 m is often more honest than a long decimal copied from a calculator.
Capacity and volume connect: 1 mL occupies 1 cm³, and 1 L is 1,000 mL. Choose litres for a drink container, but cubic metres for a large room. Always write the units beside the answer.
| Quantity | Conversion |
|---|---|
| Length | 1 km = 1,000 m; 1 cm = 10 mm |
| Area | 1 m² = 10,000 cm² |
| Volume and capacity | 1 cm³ = 1 mL; 1 L = 1,000 mL |
A common trap
Using the length conversion factor for square units: 1 m² = 100 cm².
Instead: Draw a 100 cm by 100 cm square. It contains 100 × 100 = 10,000 square-centimetre tiles.
See the thinking
Convert a length
A ribbon is 2.45 m long. Express its length in centimetres.
- One metre contains 100 centimetres.
- Multiply 2.45 by 100; the ribbon itself does not change length.
Choose honest precision
A length calculated from measurements is 3.476 m. Report it to the nearest centimetre.
- One centimetre is 0.01 m, so round metres to two decimal places.
- The third decimal is 6, so increase the hundredths digit from 7 to 8.
Check your understanding
Convert 0.8 m to millimetres.
Show answer
800 mm
There are 1,000 mm in 1 m, so 0.8 × 1,000 = 800.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- Convert 3.6 m to centimetres.1 mark
- Convert 2,750 mm to metres.2 marks
- A small floor has area 2 m². Express this in cm².2 marks
- A jug holds 1.25 L. Express this capacity in mL.1 mark
- Round 2.384 m to the nearest centimetre.2 marks
- A student reports a classroom door as 198.37291 cm high after measuring with a ruler marked in whole centimetres. Explain a more sensible report.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Convert 3.6 m to centimetres.1 mark
3.6 × 100 = 360.
360 cm - Convert 2,750 mm to metres.2 marks
1 m = 1,000 mm.
2,750 ÷ 1,000 = 2.75.
2.75 m - A small floor has area 2 m². Express this in cm².2 marks
Each square metre has 10,000 cm².
2 × 10,000 = 20,000.
20,000 cm² - A jug holds 1.25 L. Express this capacity in mL.1 mark
1.25 × 1,000 = 1,250.
1,250 mL - Round 2.384 m to the nearest centimetre.2 marks
A centimetre is 0.01 m.
The third decimal is 4, so keep the hundredths digit.
2.38 m, or 238 cm - A student reports a classroom door as 198.37291 cm high after measuring with a ruler marked in whole centimetres. Explain a more sensible report.2 marks
The instrument does not justify all the decimal places.
Round to a precision consistent with whole-centimetre readings.
About 198 cm
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 7 measurement and spatial representation: areas of triangles/parallelograms, prism volumes, circle circumference, nets and views. Precision is integrated into practical measurement; circle area is not introduced here.
Official curriculum source ↗