Converting Metric Units

The metric system is built on ten

Every metric unit is just the base unit made bigger or smaller by a power of ten. The base units are the metre (length), the gram (mass) and the litre (capacity). Adding a prefix to the front scales the unit up or down.

Prefix	Means	Example
kilo-	× 1000	1 km = 1000 m
(base)	× 1	metre, gram, litre
centi-	÷ 100	1 cm = 0.01 m
milli-	÷ 1000	1 mm = 0.001 m

Because everything scales by ten, converting never involves awkward numbers. You only ever multiply or divide by 10, 100 or 1000 — which means you are really just moving the digits, as you learned in Multiplying by 10, 100 and 1000.

The golden rule

There is one rule that decides every conversion:

Smaller unit → multiply. Bigger unit → divide.

Why? A smaller unit measures less each, so you need more of them — a bigger number — to describe the same amount. A bigger unit measures more each, so you need fewer of them.

The conversion staircase

Picture the length units as steps on a staircase, biggest at the top:

km
  \  ÷1000 going up        ×1000 going down
   m
    \  ÷100 up             ×100 down
     cm
       \  ÷10 up           ×10 down
        mm

• Going up a step (to a bigger unit) → divide.
• Going down a step (to a smaller unit) → multiply.

The key facts to memorise:

• Length: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km
• Mass: 1000 g = 1 kg
• Capacity: 1000 ml = 1 litre

Worked example 1: metres to millimetres

Convert 2.3 m into millimetres.

We are going down two steps (m → cm → mm), so we multiply twice. But it is easier to jump straight: there are 1000 mm in 1 m.

1. Smaller unit, so multiply.
2. 2.3 × 1000 = 2300 mm.

Worked example 2: grams to kilograms

Convert 4750 g into kilograms.

1. A kilogram is bigger than a gram, so divide.
2. 1 kg = 1000 g.
3. 4750 ÷ 1000 = 4.75 kg.

Worked example 3: a multi-step problem

A bottle holds 1.5 litres of juice. You pour 350 ml into a glass. How much is left, in litres?

1. Put both amounts in the same unit. Change 1.5 litres to ml: 1.5 × 1000 = 1500 ml.
2. Subtract: 1500 − 350 = 1150 ml.
3. Convert back to litres: 1150 ÷ 1000 = 1.15 litres.

Always convert to a common unit before adding or subtracting. This links closely to Adding and Subtracting Decimals.

A common mistake to avoid

Students often multiply when they should divide because they forget to check the unit size. Before you calculate, say out loud: "Am I going to a bigger or a smaller unit?" Then ask: "Should my answer be a bigger or a smaller number?" If your answer feels wrong — like a person weighing 70,000 kg — you have probably multiplied instead of divided.

Quick reference table

Convert	Operation	Example
km → m	× 1000	5 km = 5000 m
m → km	÷ 1000	2500 m = 2.5 km
m → cm	× 100	3 m = 300 cm
cm → mm	× 10	8 cm = 80 mm
kg → g	× 1000	1.2 kg = 1200 g
g → kg	÷ 1000	600 g = 0.6 kg
litre → ml	× 1000	0.4 l = 400 ml
ml → litre	÷ 1000	750 ml = 0.75 l

Why this skill matters

Unit conversion is one of the most-used skills in real life and in science. A recipe in grams, a race in kilometres, a medicine dose in millilitres — they all need converting at some point. In science lessons you will convert constantly when working with formulas, because a formula only gives the right answer when every quantity is in matching units. Master the staircase now and the rest becomes mechanical.

Try it yourself

Without a calculator, convert each of these:

1. 6 km into metres.
2. 3200 ml into litres.
3. 0.85 kg into grams.
4. 45 mm into centimetres.
5. A 2 m plank with 75 cm sawn off — what length remains, in metres?

Check your reasoning each time: smaller unit means a bigger number.

Great work!

You now know the metric prefixes, the conversion staircase, and the golden rule for multiplying or dividing. Build on it with Units of Length, Mass and Capacity or apply it to area and volume in Surface Area and Volume.