The size ladder: each step is times 10
You learn to convert length, capacity and mass with the unit ladder: each step is times 10 or divide by 10.
How to work it out
- Find the unit you start with and the unit you want on the ladder.
- Count the steps between them.
- If you go down to a smaller unit, multiply by 10 for each step.
- If you go up to a larger unit, divide by 10 for each step.
A worked example
3 m = ? cm
- Find the units on the ladder: from m to cm.
- Count the steps: m, dm, cm, so 2 steps down.
- Multiply by 10 for each step: 3 × 10 × 10 = 300.
- It is 300 cm.
More examples
25 cl = ? ml
- From cl to ml is 1 step down.
- Multiply by 10: 25 × 10 = 250.
- It is 250 ml.
2 kg = ? g
- From kg to g is 3 steps down: kg, hg, dag, g.
- Multiply by 10 for each step: 2 × 10 × 10 × 10 = 2,000.
- It is 2,000 g.
1,500 m = ? km
- From m to km is 3 steps up.
- Divide by 10 for each step: 1,500 ÷ 10 ÷ 10 ÷ 10 = 1.5.
- It is 1.5 km.
Try it yourself
From centimetre to decimetre
250 cm = ? dm
From centimetre to millimetre
40 cm = ? mm
Watch out
You go the wrong way: 3 m becomes 0.03 cm.
A smaller unit means a bigger number. A cm is small, so there are lots of them in 3 m.
You skip a step: from hl to l you multiply by 10, but the dal is in between.
Count all the steps and watch the units between your start and your end. From hl to l is 2 steps, so multiply by 100.
Tips
- Deci is a tenth, centi a hundredth and milli a thousandth.
- Kilo means thousand: from kg to g is 3 steps, so multiply by 1,000.
Why it works
On the ladder each size is ten times as small as the one above. If you go one step down, you need ten times as many small pieces. If you go up, you need ten times as few. The ladder for length (km, hm, dam, m, dm, cm, mm), volume (with litre) and weight (with gram) works exactly the same.