Unit conversions

The idea

Metric units are built on 10s, so converting is just multiplying or dividing by 10, 100 or 1,000. The key facts: 1 km = 1,000 m; 1 m = 100 cm; 1 cm = 10 mm; 1 kg = 1,000 g; 1 litre = 1,000 ml.

Going from a bigger unit to a smaller one, the number gets bigger, so multiply (3.4 km = 3.4 × 1,000 = 3,400 m). Going from smaller to bigger, the number shrinks, so divide (2,650 g = 2,650 ÷ 1,000 = 2.65 kg).

With decimals, think about the digits sliding along a place-value chart. A quick sense check helps: a door is about 2 m tall, not 200 m — if your answer looks silly, you probably went the wrong way.

Worked example

Convert 3.4 km to metres, and 2,650 g to kilograms.

1. Kilometres are bigger than metres, so multiply: 3.4 × 1,000.
2. 3.4 × 1,000 = 3,400, so 3.4 km = 3,400 m.
3. Grams are smaller than kilograms, so divide: 2,650 ÷ 1,000.
4. 2,650 ÷ 1,000 = 2.65, so 2,650 g = 2.65 kg.

Answer: 3,400 m; 2.65 kg

Watch out

• Multiplying when you should divide — always ask whether the answer should be a bigger or smaller number.
• Using ×100 for kilometres to metres (it is ×1,000).
• Sliding the decimal point the wrong number of places, e.g. writing 4.07 litres as 407 ml instead of 4,070 ml.