MISSION · Measurement
Converting Units of Measure
Why the answer changes size when the unit does
LEVEL 1 · EXPLORE
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LEVEL 2 · LEARN
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The idea in one sentence
The amount stays the same; only the size of the ruler changes, so a smaller unit always gives a bigger number.
Small unit, big number
A pencil is 15 centimetres long. It is also 150 millimetres long, and 0.15 metres long. Nothing about the pencil changed between those three sentences.
That’s the whole logic of conversion. Measuring with a smaller unit means it takes more of them to cover the same distance. Millimetres are the smallest of the three, so the millimetre answer is the biggest number. If you convert to a smaller unit and your number gets smaller, you’ve multiplied when you should have divided.
The metric ladder
The metric system was built to make this easy: every step is a factor of ten.
| Unit | In metres | Handy for |
|---|---|---|
| millimetre (mm) | 0.001 | Rain, screws, the thickness of a coin |
| centimetre (cm) | 0.01 | Pencils, hands, a book |
| metre (m) | 1 | Rooms, people, a swimming pool |
| kilometre (km) | 1000 | Journeys, rivers, a run |
The same prefixes do the same job for mass and capacity: a kilogram is a thousand grams, a millilitre is a thousandth of a litre. Learn the prefixes once and they work everywhere — kilo means a thousand of them, centi means a hundredth, milli means a thousandth.
How to know whether to multiply or divide
Ask which unit is smaller before you touch the numbers.
- Going to a smaller unit — metres to centimetres — multiply. More of them fit.
- Going to a bigger unit — centimetres to metres — divide. Fewer of them fit.
Then sanity-check the result. Converting 3 metres to centimetres should not give 0.03. A room is not three-hundredths of anything.
Units have to match before you calculate
You cannot add 3 metres to 40 centimetres and write 43 of something. Convert first — 340 cm, or 3.4 m — and then add. This is the single most common place a measurement answer goes wrong, and it usually happens in a word problem where the two measurements are given in different units on purpose.
The answer also needs its unit attached. “7” is not a length.
Common mix-ups
- Multiplying when you should divide. Check the direction against “smaller unit, bigger number” every time.
- Miscounting the zeros. Metres to millimetres is two steps — ×100 — not ×10.
- Adding across units without converting first.
- Dropping the unit from the answer, which makes it unreadable and unmarkable.
Check yourself
A ribbon is 2.5 metres long. How many centimetres is that? How many pieces of 20 cm can you cut from it?
\(2.5 \times 100 = 250\) cm, because centimetres are smaller so the number grows. \(250 \div 20 = 12\) pieces, with 10 cm left over.
LEVEL 3 · REFLECT
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