Measurement (Length) • Topic 3 of 5

Conversion of Units

Because the metric system is built on powers of ten, converting between units is just multiplying or dividing by 10, 100 or 1000 - no awkward factors to memorise. The single rule that covers everything: going from a LARGER unit to a SMALLER unit, you MULTIPLY; going from a SMALLER unit to a LARGER unit, you DIVIDE. Picture a ladder with km at the top, then m, then cm, then mm at the bottom. Stepping down the ladder multiplies; stepping up divides. The factors are fixed: km to m multiply by 1000 (5 km = 5000 m); m to cm multiply by 100 (4 m = 400 cm); cm to mm multiply by 10 (7 cm = 70 mm). Reverse each one to go up: cm to m divide by 100 (450 cm = 4.5 m); m to km divide by 1000 (3500 m = 3.5 km); mm to cm divide by 10 (80 mm = 8 cm). Compound or mixed measurements like 3 m 45 cm are handled by converting the larger part first, then adding: 3 m = 300 cm, plus 45 cm, gives 345 cm. The errors children make are predictable - multiplying when they should divide, or slipping a decimal point. The fix is to tie conversion to place value (each step is a power of ten, so the decimal point simply shifts) and to keep a direction chart on the wall: down the ladder multiply, up the ladder divide. Always insist the answer carries its unit; a bare number is not a measurement.

✅ Solved examples

1. Convert 3 m 45 cm into centimetres.
Convert the metres first: 3 m = 3 x 100 = 300 cm. Then add the loose centimetres: 300 + 45 = 345 cm. Larger unit to smaller, so we multiplied.
2. Convert 4500 m into kilometres.
Metre to kilometre is smaller to larger, so divide by 1000: 4500 / 1000 = 4.5 km (that is 4 km 500 m).
3. A ribbon is 7 cm long. How many millimetres is that?
Centimetre to millimetre is larger to smaller, so multiply by 10: 7 x 10 = 70 mm.
4. Convert 5 km 250 m into metres.
Convert the kilometres first: 5 km = 5 x 1000 = 5000 m. Add the remaining metres: 5000 + 250 = 5250 m.

✏️ Practice — try these, take hints as needed

1. Convert 2.5 m into centimetres.
m to cm is larger to smaller.
Multiply by 100.
250 cm
2. Convert 350 cm into metres.
cm to m is smaller to larger.
Divide by 100.
3.5 m (3 m 50 cm)
3. A child writes 1 m = 10 cm. What is the correct value, and what should the teacher reinforce?
Count the marks on a metre rod.
It is a power of ten, but which one?
1 m = 100 cm; have the child count the 100 cm marks on a metre rod
4. Convert 3 km into metres.
km to m is larger to smaller.
Multiply by 1000.
3000 m

📝 Topic test — 8 questions

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