Converting units
We convert units by multiplying or dividing by how many of the smaller unit fit into the bigger one: 3.5 m = 350 cm. For area the factor is used twice, for volume three times. One litre is one cubic decimetre.
Watch Fox work it out on the board
Fox works one step at a time. Press play.
A smaller unit gives a bigger number
We want to write the same amount in a different unit.
| Prefix | Means | Examples |
|---|---|---|
| kilo (k) | 1 000 | 1 km = 1 000 m, 1 kg = 1 000 g |
| hecto (h) | 100 | 1 hg = 100 g |
| deci (d) | one tenth, 0.1 | 1 dm = 0.1 m, 1 dl = 0.1 l |
| centi (c) | one hundredth, 0.01 | 1 cm = 0.01 m, 1 cl = 0.01 l |
| milli (m) | one thousandth, 0.001 | 1 mm = 0.001 m, 1 ml = 0.001 l |
- To a smaller unit: multiply. The number gets bigger.
- To a bigger unit: divide. The number gets smaller.
1 m = 10 dm = 100 cm = 1 000 mm 1 km = 1 000 m
Area, volume and litres
Area has two directions, length and width. That is why the length factor is used twice.
1 m² = 100 cm · 100 cm = 10 000 cm²
1 m² = 100 dm² = 10 000 cm² 1 dm² = 100 cm² = 10 000 mm²
Volume has three directions, so the factor is used three times: 10 · 10 · 10 = 1 000. One cubic decimetre holds exactly one litre.
| Cubic unit | Litres |
|---|---|
| 1 m³ = 1 000 dm³ | = 1 000 l |
| 1 dm³ = 1 000 cm³ | = 1 l = 10 dl |
| 1 cm³ | = 1 ml |
Time does not follow base ten
One hour is 60 minutes, not 100. That is why we cannot move the decimal point.
0.5 h = 0.5 · 60 min = 30 min
So 1.5 h = 1 h 30 min = 90 min.
Example
Example 1: 2.4 m² in square centimetres
We want to write the area in the smaller unit cm².
1 m² = 100 cm · 100 cm. The factor is 10 000, not 100.
1 m² = 10 000 cm²
We multiply 2.4 by 10 000.
2.4 m² = 2.4 · 10 000 cm² = 24 000 cm²
A rectangle measuring 2 m · 1.2 m has an area of 2.4 m². In centimetres: 200 · 120 = 24 000 cm². The same answer.
Example 2: how many litres does a fish tank measuring 50 cm · 30 cm · 40 cm hold?
We want the volume in litres. Because 1 dm³ = 1 litre, we work in decimetres.
10 cm is 1 dm, so we divide each measurement by ten.
50 cm = 5 dm, 30 cm = 3 dm, 40 cm = 4 dm
Volume is length times width times height.
5 dm · 3 dm · 4 dm = 60 dm³
One cubic decimetre is one litre.
60 dm³ = 60 litres
In centimetres: 50 · 30 · 40 = 60 000 cm³ = 60 000 ml = 60 litres. The same answer.
Pitfalls
Using the length factor for area: 2 m² = 200 cm².
Area has two directions: 100 · 100 = 10 000. So 2 m² = 20 000 cm².
Dividing when we should multiply: 4 km = 0.004 m.
The metre is a smaller unit, so the number should get bigger: 4 km = 4 · 1 000 m = 4 000 m.
Reading 1.5 hours as 1 hour and 50 minutes.
One hour has 60 minutes: 0.5 · 60 = 30. So 1.5 h = 1 h 30 min.
Practise on your own
0 of 4 correct1How many grams is 4.2 kg?
2How many litres is 750 ml?
3How many cm² is 0.5 m²?
4A box is 20 cm long, 15 cm wide and 10 cm high. How many litres does it hold?
More walkthroughs with Fox
Common questions
How many cm² are there in one m²?
10 000. One square metre is 100 cm long and 100 cm wide, and 100 · 100 = 10 000.
How many litres are there in one cubic metre?
1 000 litres. One cubic metre is 10 · 10 · 10 = 1 000 dm³, and each cubic decimetre is one litre.
How do you convert hours in decimal form to minutes?
Multiply the decimal part by 60: 1.25 h is 1 h and 0.25 · 60 = 15 min, so 75 minutes.
Why does the number get bigger when you change to a smaller unit?
The amount is the same, but each small unit holds less. So we need more of them: 1 m = 100 cm.
Read also
- Years 4–9Area and perimeterHow do you work out area and perimeter?
- Years 5–9Volume of a cuboid, prism and cylinderHow do you work out volume?
- Years 5–9Scale: maps, drawings and enlargementsHow do you calculate with scale?
- Years 5–9Fractions, decimals and percentagesHow do you convert fractions to decimals and percentages?
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