Metric Unit Conversions

In the exam you are often asked to change a measurement into a different unit, such as a length in metres into centimetres. These questions are worth 1 mark and usually come early in the paper.

Longer questions, for 2 or 3 marks, mix units in one problem: litres and millilitres, kilograms and grams, or hours and minutes. Change to matching units, do the calculation, then give your answer in the unit the question asks for.

Paper 1 has no calculator, so practise multiplying and dividing by 10, 100 and 1000 in your head. Units such as ounces, pints and miles are not metric. When a question uses them, it tells you how to convert them.

A unit says what a number measures. A pencil might be 15 cm long, but a walk of 15 km takes hours. Converting describes the same amount in a different-sized unit.

• Length: 10 mm =1 cm, 100 cm =1 m and 1000 m =1 km.
• Mass: 1000 g =1 kg and 1000 kg =1 tonne.
• Capacity: 1000 ml =1 litre.
• Time: 60 seconds =1 minute and 60 minutes =1 hour.

The metric units go up in tens, hundreds and thousands. Time is different: it goes up in sixties.

Changing to a smaller unit, you need more of them, so the number gets bigger. Multiply: 3 metres is 3\times100=300 centimetres.

Changing to a bigger unit, you need fewer of them, so the number gets smaller. Divide: 4500 grams is 4500\div1000=4.5 kilograms.

Multiplying by 100 moves every digit two places to the left, so 2.7\times100=270. Dividing by 1000 moves every digit three places to the right, so 650\div1000=0.65

Always ask whether your answer is sensible. A door about 2 m tall is about 200 cm tall, not 0.02 cm.

Before you add, subtract or compare two measurements, change them to the same unit. You cannot take 650 grams away from 2.5 kilograms by working out 2.5-650.

Changing into the smaller unit usually gives whole numbers, which are easier to work with. At the end, read the question again and give your answer in the unit it asks for.

To change hours into minutes, multiply by 60: 3 hours is 3\times60=180 minutes. To change minutes into hours and minutes, take out as many sixties as you can: 200 minutes is 3 hours 20 minutes, because 200-180=20.

A decimal part of an hour is not a number of minutes. Half an hour, 0.5 hour, is half of 60 minutes, which is 30 minutes, not 50 minutes. Multiply the decimal part by 60 to find the minutes.

Keep a length of time, such as 90 minutes, separate from a clock time, such as 10:30. Add the length of time to the starting time to find when something finishes.

• Using the wrong conversion number. There are 10 mm in a centimetre, 100 cm in a metre and 1000 ml in a litre.
• Multiplying when you should divide. Changing to a smaller unit makes the number bigger; changing to a bigger unit makes it smaller.
• Mixing units in one calculation. Change both measurements to the same unit before you add or subtract.
• Giving the answer in the wrong unit. Check which unit the question asks for, and convert at the end if you need to.
• Reading a decimal of an hour as minutes. Multiply the decimal part by 60, so 0.7 of an hour is 42 minutes.
• Rounding up the number of full containers. Count only the containers that can be filled completely.