Converting Between Metric Units

The metric system uses the same conversion rule as the English one, but with a decisive advantage: every factor is a power of ten. There is no 12, no 5280 — only 10, 100 and 1000.

Concept The three base units

The metre (m) measures length.

The litre (L) measures volume.

The kilogram (kg) measures mass.

The system takes its name from the metre, the reference unit that replaced each country's own local measures.

Concept The conversion factors

1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, so 1 m = 1000 mm. Volume and mass follow the same pattern: 1 L = 1000 mL and 1 kg = 1000 g.

Theorem The same ratio rule

\text{conversion ratio} = \frac{\text{unit you want}}{\text{unit you are removing}}

Nothing changes from the English system except the numbers. Because those numbers are powers of ten, converting amounts to moving the decimal point.

Example 2.5 metres into centimetres

2.5 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}}

The metres cancel, leaving centimetres.

2.5 \times 100 = 250

⟹ 250 centimetres

Example Three everyday conversions

A 1.5 litre bottle, a 2500 gram bag of rice, and a 3.2 kilometre race.

1.5 \times 1000 = 1500

⟹ 1500 millilitres

2500 \div 1000 = 2.5

⟹ 2.5 kilograms

3.2 \times 1000 = 3200

⟹ 3200 metres

Each answer came from multiplying or dividing by 1000 — in effect, sliding the decimal point three places.

Note What the prefixes mean

kilo- means 1000 of the unit.

centi- means one hundredth of it.

milli- means one thousandth of it.

The prefixes keep their meaning across every base unit, so a kilogram relates to a gram exactly as a kilometre relates to a metre. Note also that what we loosely call weight in daily life is, strictly, mass.

Summary

The base units are the metre, the litre and the kilogram.
1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
1 L = 1000 mL and 1 kg = 1000 g.
The ratio rule is unchanged: wanted unit on top, unwanted unit below.
Every factor is a power of ten, so converting just shifts the decimal point.