Converting Units in Problems

Amounts in different units cannot be added. Convert them all to one unit first.

Which way to go

To a smaller unit, multiply. To a bigger unit, divide.

Decimals help

250 ml is 0.25 litres. Either unit works, as long as everything matches.

The check that works

Smaller unit, bigger number. If your number went the wrong way, so did you.

Convert before you calculate

A problem mixing 2.5 metres and 40 centimetres cannot be added until both are in one unit. Convert everything first, then do the arithmetic. Trying to convert partway through is how numbers end up in the wrong unit without anyone noticing.

Choosing which unit to use

Convert to whichever unit avoids decimals if you can, or to whichever the answer is wanted in. For 2.5 m and 40 cm, working in centimetres gives 250 and 40 — both whole numbers, and easier to handle than 2.5 and 0.4.

Which way to multiply

Converting to a smaller unit gives a bigger number, so multiply. Converting to a bigger unit gives a smaller number, so divide. Decide the direction before touching the arithmetic; getting it backwards produces an answer off by a factor of a hundred or a thousand.

Label every number

Write the unit next to every number in your working, not just the final answer. In a multi-step problem with mixed units, an unlabelled number is a mistake waiting to happen — and labelling is what makes the mistake visible before it propagates.