These questions ask you to choose a metric factor and direction for a length, area or volume. Some also ask you to convert before or after finding a geometric measurement and confirm that both routes agree.
Let the dimension choose the factor
| Measurement | Conversion rule and quick example |
|---|---|
| Length | One metre is 100 centimetres, one centimetre is 10 millimetres, and one kilometre is 1000 metres. Thus 4.2 metres is 420 centimetres. |
| Area | The metre-to-centimetre factor is used in two directions, so 1 m² is 10 000 cm². Thus 1.2 m² is 12 000 cm². |
| Volume | The centimetre-to-millimetre factor is used in three directions, so one cubic centimetre is 1000 cubic millimetres. Thus 2.5 cubic centimetres is 2500 cubic millimetres. |
| Capacity | One litre is 1000 cubic centimetres. Thus 4500 cubic centimetres is 4.5 litres. |
For a rectangle, you may convert each side first and then multiply, or find the area first and convert the finished area. For example, 300 centimetres by 120 centimetres becomes 3 metres by 1.2 metres, giving an area of 3.6 m²; the route through 36 000 cm² gives the same result after division by 10 000.
Conversion traps to avoid
| Tempting route | How to reject it |
|---|---|
| Use the factor from a neighbouring metric step | Name both units before calculating. Metres to centimetres uses 100, while centimetres to millimetres uses 10. |
| Multiply when moving from small units to large units | Larger units need fewer pieces, so divide. Smaller units need more pieces, so multiply. |
| Use a length factor once on an area | An area has two directions. Multiply the linear factor by itself, making 100 become 10 000. |
| Use a length or area factor on a volume | A volume has three directions. A factor of 10 becomes 10 times 10 times 10, not 10 or 100. |
| Use the area factor for a perimeter | Perimeter is a length around an edge, so its unit changes only once. Area units are not involved. |
Try it
A pencil is 7 centimetres long. Enter its length in millimetres.
A tank has an internal volume of 3000 cubic centimetres, and one litre fills 1000 cubic centimetres. How many litres does the tank hold?
- 30 litres
- 3000 litres
- 0.3 litres
- 3 litres
A rectangular tabletop measures 200 centimetres by 150 centimetres. Select all the statements that are true about the area of this tabletop in square metres.
- It is 3 square metres.
- It is 300 square metres, because a square metre is one hundred square centimetres.
- It is 30 square metres.
- Converting each side first, 2 metres by 1.5 metres leads to the very same result.