From a millimetre to a kilometre
How long is a pencil? About 15 centimetres. How high is a door? About 2 metres. How far is it to grandma’s? Maybe 30 kilometres. For differently sized things we have differently sized units — so that the numbers come out sensible.
The ladder of length units, from the smallest:
- millimetre (mm) — the thickness of a coin,
- centimetre (cm) = 10 mm — the width of a fingernail,
- metre (m) = 100 cm — a big step,
- kilometre (km) = 1 000 m — a quarter of an hour of brisk walking.
Converting means saying the same length in another unit: 3 m = 300 cm. The length has not changed, you only measure with a different metre.
The rule is one: to a smaller unit you multiply, to a bigger one you divide. A smaller unit means more pieces — so times. And times by ten and a hundred you already know perfectly.
Adam is building a shelf with dad and in the instructions it says: board 120 cm. Dad has a metre (folding) and asks Adam: “How many metres is that?” Adam counts: 100 cm is a metre, so 120 cm is a metre and 20 cm. Dad unfolds the metre, measures, cuts. Then Adam measures the thickness of the board: on the ruler 18 small marks — 18 mm. “And in centimetres?” dad asks. Ten millimetres is a centimetre… 18 mm = 1 cm and 8 mm. The shelf holds and Adam knows two conversions from real life.
Remember three steps: 10 – 100 – 1 000. From mm to cm it is 10, from cm to m it is 100, from m to km it is 1 000.
How to convert: smaller unit = times, bigger = divided by
Direction down (to a smaller unit) → multiply:
- m → cm: times 100. Example: 3 m = 3 × 100 = 300 cm.
- cm → mm: times 10. Example: 7 cm = 70 mm.
- km → m: times 1 000. Example: 2 km = 2 000 m.
Why times? A metre splits into 100 centimetre pieces. More pieces = a bigger number.
Direction up (to a bigger unit) → divide:
- cm → m: divided by 100. Example: 500 cm = 5 m.
- mm → cm: divided by 10. Example: 40 mm = 4 cm.
- m → km: divided by 1 000. Example: 8 000 m = 8 km.
When it does not come out smoothly, use a mixed write-up:
250 cm = 200 cm + 50 cm = 2 m 50 cm.
1 500 m = 1 000 m + 500 m = 1 km 500 m.
Method for every conversion:
- Decide the direction: to a smaller, or to a bigger unit?
- Find the step: 10, 100, or 1 000?
- Multiply, or divide.
- Check the sense: in smaller units a bigger number must come out.
To a smaller unit
Convert: 4 m to cm, 12 cm to mm, 3 km to m.
4 m → cm: smaller unit → I multiply. The step m–cm is 100. 4 × 100 = 400 cm.
12 cm → mm: step 10. 12 × 10 = 120 mm.
3 km → m: step 1 000. 3 × 1 000 = 3 000 m.
Sense check: the numbers grew (400 > 4). It fits — there are more small pieces.
To a bigger unit
Convert: 600 cm to m, 90 mm to cm, 5 000 m to km.
600 cm → m: bigger unit → I divide. 600 ÷ 100 = 6 m.
90 mm → cm: 90 ÷ 10 = 9 cm.
5 000 m → km: 5 000 ÷ 1 000 = 5 km.
Sense check: the numbers got smaller. It fits — you need fewer big units.
Mixed write-up
Convert 173 cm (dad’s height) to metres and centimetres.
Step 1: how many whole metres? 100 cm is a metre, 200 cm would already be two — dad has one whole metre.
Step 2: remainder: 173 − 100 = 73 cm.
Write-up: 1 m 73 cm.
And back: 2 m 5 cm = 200 cm + 5 cm = 205 cm. Watch the zero: 2 m 5 cm is not 25 cm! The metres brought two hundred, the five sits alone on the ones.
Always write the unit next to the number. Plain “300” means nothing — 300 mm is the length of a ruler, 300 km is a trip across half the country. And with a mixed write-up watch: 2 m 5 cm = 205 cm, not 25 cm.
Practice: now you do it 🎲
Now try it for real. You will see all the questions at once, like on paper. 开始 with ten. When it goes well, add more.
Convert: decide the direction, find the step (10, 100, 1 000), multiply or divide.
On paper
Half the work is with a ruler — measuring is the best teacher of units.
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Measure with a ruler three things on the table (a pencil, a rubber, a notebook) and write each in cm and mm.
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Convert: 5 m to cm, 30 mm to cm, 4 km to m, 800 cm to m.
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Write mixed: 340 cm = ☐ m ☐ cm, 1 250 m = ☐ km ☐ m.
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Estimate without measuring the height of a door and the length of your step, then (with a metre if you like) check. Write the estimate and the real thing.
Now you 💪
- You can say the ladder: mm → cm → m → km with steps 10, 100, 1 000.
- You know when to multiply and when to divide — and you can explain it with pieces.
- You convert 250 cm to 2 m 50 cm and back.
Done when: You convert between mm, cm, m and km both ways and you check the result with common sense.
What to take from this lesson
- Length ladder: mm, cm, m, km. Steps: 10, 100, 1 000.
- To a smaller unit multiply, to a bigger one divide.
- Sense check: smaller units → bigger number.
- Does it not come out smoothly? Mixed write-up: 250 cm = 2 m 50 cm.
- A number without a unit is mute — always write the unit.
© 2026 Ing. Martin Polak / AlgoRhino · 内容使用条款