To convert an area, square the length conversion factor. To convert a volume, cube it. That single rule explains why 1 m² is 10 000 cm² and why 1 m³ is 1 000 000 cm³.
What is the small gap?
Students learn “×100 for m to cm” and then apply it to m² as well. The length factor is right for a length, but an area is a length times a length, so the factor acts twice.
Why does squaring work?
Picture a square 1 m by 1 m. Cut each side into 100 pieces of 1 cm. You get a grid of 100 rows, each with 100 small squares.
| Unit | In smaller unit | Why |
|---|---|---|
| 1 m | 100 cm | length |
| 1 m² | 10 000 cm² | 100 × 100 |
| 1 m³ | 1 000 000 cm³ | 100 × 100 × 100 |
A scaffolded example
An original problem: a notice board has an area of 0.8 m². Give its area in cm².
The length factor is 100, so the area factor is 100² = 10 000. Area = 0.8 × 10 000 = 8000 cm².
Check by lengths: if the board is 1 m by 0.8 m, that is 100 cm by 80 cm, and 100 × 80 = 8000 cm². They agree.
What does the common mistake look like?
A student writes 0.8 × 100 = 80 cm². That answer says a board of 80 cm² is about the size of a large postcard, not a notice board. Check that the number has a sensible size: if the unit gets smaller, the number must get much bigger.
Self-check
A fish tank holds 54 000 cm³ of water. How many litres is that? And how many m³?
Answer
Litres: 1 litre = 1000 cm³, so 54 000 ÷ 1000 = 54 litres. m³: 1 m³ = 1 000 000 cm³, so 54 000 ÷ 1 000 000 = 0.054 m³.
Check: a cubic metre holds 1000 litres, so 54 litres should be a small fraction of it. 54 ÷ 1000 = 0.054, which matches.
Where does this show up in SPM?
In SPM Mathematics, it appears in mensuration and scale drawings. In Physics, density and pressure calculations mix cm³ and m³, and a slip changes the answer by a factor of a million.
Continue with perimeter, area and volume or see converting units in a rate for the same idea with speed. The geometry and measurement hub shows the whole sequence.
One-to-one Mathematics tuition starts with a one-hour trial class (from RM50).