Length conversions
We use four main units of length every day: millimetre (mm), centimetre (cm), metre (m) and kilometre (km). Each one suits a different size of thing.
What each unit fits
- mm — tiny things: a fingernail is about 12 mm thick.
- cm — small objects: a pencil is about 18 cm long.
- m — rooms and people: you are probably around 1.4 m tall.
- km — long journeys: the distance to school might be 2 km.
The ladder
| Step | Equality |
|---|---|
| mm → cm | 10 mm = 1 cm |
| cm → m | 100 cm = 1 m |
| m → km | 1 000 m = 1 km |
So a metre has 1 000 mm in it, and a kilometre has 100 000 cm. Big numbers — that is exactly why we have the bigger units.
Going down the ladder — multiply
Bigger unit to smaller unit: more pieces fit in, so the number grows.
5 m = ? cm
There are 100 cm in 1 m, so:
5 m = 5 × 100 cm = 500 cm.
3 km = ? m
3 km = 3 × 1 000 m = 3 000 m.
Going up the ladder — divide
Smaller unit to bigger unit: fewer big pieces fit in, so the number shrinks.
4 500 m = ? km
4 500 ÷ 1 000 = 4.5 km (four and a half kilometres).
80 cm = ? m
80 ÷ 100 = 0.8 m.
💡 Trick for ×10, ×100, ×1 000: just slide the decimal point or add zeros.
Mixed units in a single problem
Sometimes a problem mixes two units in one sentence. Pick one unit and convert everything to it before you compute.
A piece of ribbon is 1 m 25 cm long. We cut off 40 cm. How much is left?
Step 1 — convert to a single unit. 1 m 25 cm = 100 cm + 25 cm = 125 cm.
Step 2 — subtract. 125 − 40 = 85 cm.
You could also turn 40 cm into 0.4 m and work in metres: 1.25 m − 0.4 m = 0.85 m. Either way works.
Imperial units (good to know)
In the United States and the United Kingdom you will also meet inches, feet, yards and miles.
| Unit | Equality |
|---|---|
| 1 foot | 12 inches |
| 1 yard | 3 feet |
| 1 mile | 1 760 yards |
These don't sit on a ladder of tens, so you have to remember each step. Year 4 only needs the basics: an inch is about 2.5 cm; a mile is a little over 1.5 km.
What's next
- Mass and volume — same ladder idea, different stuff to measure
- Time conversions — a different ladder that uses 60s
- Back to the introduction