Converting from a larger unit to a smaller one

Whenever you go from a larger unit (km) to a smaller unit (m, cm, mm), you always multiply. The reason is simple: a smaller unit is a smaller measuring stick, so you need more of them to cover the same distance.

The rule

To convert from a larger unit to a smaller unit, multiply by the conversion factor.

Metric examples

Imperial examples

Why it always gives a whole number

If you start with a whole number of larger units, the result of multiplication by an integer factor will also be a whole number. That is why our exercises stick to whole-number inputs — there is never a remainder to worry about.

For example: $5\text{km}\times 1000=5000\text{m}$. The result has trailing zeros precisely because you multiplied by a thousand.

Common pitfalls

• Skipping a step. Going km → cm in one go is a jump of $\times 100000$. Many students forget zeros. If you are unsure, do it in two steps: km → m, then m → cm.
• Mixing up directions. Always ask yourself: am I going to a smaller stick? Then multiply. To a longer stick? Then divide.
• Imperial factors. They are not all the same — 12, 3 and 1 760. There is no shortcut here, you simply have to remember them.

Read more

• Length unit conversions – guide
• Metric system
• Imperial units
• Converting smaller to larger

Practise

• Convert larger to smaller (metric)
• Convert two units to one
• Imperial – larger to smaller