Paper Together: sit a paper in a room with your friends.See how it works
This page sets out the method for conversions & units in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Conversions & units topic page.
When you see cm² or cm³, do not use the length factor on its own — square or cube it.
When you see miles, pounds, gallons, feet or inches, use the approximate fact given (or the standard one) as a ratio.
1 km = 1000 m. 1 m = 100 cm. 1 cm = 10 mm.
1 kg = 1000 g. 1 litre = 1000 ml.
To go to a smaller unit, multiply.
To go to a larger unit, divide.
1.2 m in mm is 1.2 × 100 = 120 cm, then × 10 = 1200 mm.
Or one jump of × 1000 from metres to millimetres.
1 m² = 100 × 100 = 10 000 cm².
Length converts by 100. Area converts by 100 squared.
60 seconds in a minute, 60 minutes in an hour.
Do not multiply time by 10 or 100.
If the lengths are in different units, convert them before you find an area or a perimeter.
A 2 m side and a 40 cm side are not 2 × 40.
Metric length is built from tens. 1cm=10mm, 1m=100cm, and 1m=1000mm. 1km=1000m. To move to a smaller unit, multiply. 3.5m× 100=350cm. To move to a larger unit, divide. 4500mm÷ 1000=4.5m. A quick picture is a metre stick: it holds 100 centimetre gaps, so the centimetre number is 100 times the metre number.
Chain two steps when the units are far apart. 2m in millimetres is 2× 100=200cm, then 200× 10=2000mm. That is the same as 2× 1000=2000. Do not multiply by 100 and by 10 and also by 1000. Pick one path. If you are unsure of the direction, test 1 unit. You know 1m is longer than 1cm, so the number of centimetres in a metre must be more than 1. That tells you to multiply.
Write the unit on every line, not only at the end. A bare 350 could be centimetres, millimetres or metres. The sentence 3.5m=350cm shows both the factor and the direction. The same habit catches a slip such as 3.5× 10=35, which would be right for centimetres into millimetres but wrong for metres into centimetres. Keep a short list in your book: × 10 for centimetres to millimetres, × 100 for metres to centimetres, × 1000 for metres to millimetres or kilometres to metres.
Method: 1. Multiply to reach a smaller unit, and divide to reach a larger unit. 2. Change metres to centimetres with × 100, so 3.5m=350cm. 3. Change metres to millimetres with × 1000, so 2m=2000mm.
An area unit is a square whose side is one length unit. Change the side, then square. Because 1m=100cm, a square metre is a square of side 100cm, and 100× 100=10000. So 1m^2=10000cm^2. Then 2.4m^2=2.4× 10000=24000cm^2. Multiplying 2.4 by 100 only would give 240, which is the conversion for a length of 2.4m, not for an area.
The same idea works for smaller steps. 1cm=10mm, so 1cm^2=10× 10=100mm^2. Therefore 3.2cm^2=3.2× 100=320mm^2. Between m^2 and mm^2 the length factor is 1000, and 1000^2=1000000, so 1m^2=1000000mm^2. Whenever the unit has a square, square the length factor. Whenever it does not, use the length factor once.
Method: 1. Square the length factor before you multiply an area. 2. Because 1m=100cm, 1m^2=10000cm^2, and 2.4m^2=24000cm^2. 3. Because 1cm=10mm, 1cm^2=100mm^2.
Volume multiplies three lengths, so the conversion factor is used three times. 1m=100cm gives 1m^3=100^3=1000000cm^3. 1cm=10mm gives 1cm^3=10^3=1000mm^3. A cuboid measured in mixed units is a trap. Convert every edge into the unit you want, then multiply. Edges of 0.8m, 0.5m and 0.4m become 80cm, 50cm and 40cm.
Now the volume is ordinary multiplication: 80× 50=4000, and 4000× 40=160000cm^3. If you had multiplied the metre lengths first, 0.8× 0.5× 0.4=0.16m^3. That is the same space. To see why, convert 0.16m^3 by the cube factor: 0.16× 1000000=160000cm^3. Either route works. Mixing them, such as multiplying 0.8m by 50cm by 40cm, does not, because the factors have only been applied to some of the edges.
Method: 1. Cube the length factor, or convert every edge before you multiply. 2. Edges 0.8m, 0.5m and 0.4m become 80cm, 50cm and 40cm. 3. The volume is 80× 50× 40=160000cm^3, the same as 0.16m^3.
A litre is a capacity unit tied to cubic centimetres: 1 litre=1000cm^3. To change cubic centimetres into litres, divide by 1000. The cuboid of volume 160000cm^3 holds 160000÷ 1000=160 litres. To change litres into cubic centimetres, multiply by 1000. A bottle of 1.5 litres holds 1500cm^3. This factor is 1000, not 10000, because it links a named capacity unit to cm^3. It is not the square factor from metres to centimetres.
A cubic metre is a large volume. Since 1m^3=1000000cm^3 and each litre is 1000cm^3, one cubic metre holds 1000000÷ 1000=1000 litres. A tank of 0.2m^3 holds 0.2× 1000=200 litres. You can remember the pair as 1m^3=1000 litres and 1 litre=1000cm^3. Use the pair that matches the units already in the question, and still cube a length factor if you convert the edges yourself. A small check keeps the factors apart: a length of 4.5m is 450cm, an area of 4.5m^2 is 45000cm^2, and a volume of 4.5m^3 is 4.5× 1000000=4500000cm^3, which is 4500 litres. Same starting number, three different factors, because one dimension, two dimensions and three dimensions are not the same kind of measure.
Method: 1. Divide cubic centimetres by 1000 to get litres. 2. So 160000cm^3=160000÷ 1000=160 litres. 3. Use 1m^3=1000 litres, so 0.2m^3=200 litres.
Most lost marks in unit questions come from multiplying when the number should be divided. Use a simple size check. If you change to a smaller unit, there must be more of them, so the number gets bigger and you multiply. If you change to a larger unit, there are fewer of them, so the number gets smaller and you divide. Say it out loud: "3.5 m is a lot of centimetres, so multiply by 100".
Write the conversion fact as an equation before you use it, for example 1 m = 100 cm or 1 km = 1000 m. Then the multiply or divide choice is clear from the fact. For awkward conversions, go through a middle unit: mm to cm to m. This adds a line of working but makes arithmetic slips much less likely.
Method: 1. Write the conversion fact you need, such as 1 km = 1000 m. 2. Decide if the new unit is smaller (multiply) or larger (divide). 3. Carry out the calculation and write the new unit. 4. Check that the size of the number makes sense for the new unit.
Tip: A smaller unit gives a bigger number. A bigger unit gives a smaller number.
A compound unit has two units in it, such as metres per second or grams per cubic centimetre. You convert each part separately. To change km/h into m/s, change the kilometres into metres (× 1000) and the hours into seconds (÷ 3600). Together this is ÷ 3.6. To go back from m/s to km/h, multiply by 3.6.
For density, 1 g/cm^3 = 1000 kg/m^3. This is because 1 m^3 is 1 000 000 cm^3 but a kilogram is only 1000 g, so the net effect is a factor of 1000. Exam questions often ask for the mass of an object in kilograms, so convert the volume into the same unit that the density uses before you multiply.
Method: 1. Split the compound unit into its top part and its bottom part. 2. Convert each part with its own conversion fact. 3. Combine the two factors, or use the shortcut 3.6 for speeds and 1000 for density. 4. Use the matching units: if density is in g/cm^3, the volume must be in cm^3.
Tip: For speed: km/h to m/s divide by 3.6. For m/s to km/h multiply by 3.6.
Exam questions combine units with a context: how many paving slabs fit a patio, how long a tap takes to fill a tank, or what a tank holds in litres. The length factor 100 becomes 100^2 = 10 000 for area and 100^3 = 1 000 000 for volume. A faster route is to convert every length to the same unit first, and then calculate the area or volume directly in that unit.
For capacity, remember 1 litre = 1000 cm^3 and 1 m^3 = 1000 litres. Rate problems divide the volume by the rate to get a time, and the answer may need turning into hours and minutes. If the time comes out as 160 minutes, write it as 2 hours 40 minutes, because 160 ÷ 60 = 2 remainder 40.
Method: 1. Convert every length to one unit before you multiply. 2. Work out the area or volume in that unit. 3. Convert to litres or square metres only if the question needs it. 4. For time, divide the volume by the rate and change minutes into hours and minutes.
Unit questions in exams often use the wording "Show that 90 km/h is 25 m/s" or "Is the speed greater than 90 km/h?". For a "show that", you must write the full calculation that reaches the stated value, not just the answer. For a comparison, change both quantities to the same unit and then compare them with a clear sentence.
Choose the unit that needs the fewest conversions. If one quantity is already in metres per second, convert the other one to m/s rather than converting both. Round only at the end, and quote enough digits to make the comparison clear. If two values are very close, such as 98.2 and 90, say which one is larger and by how much.
Method: 1. Pick one unit for the comparison and say what it is. 2. Convert the other quantity with a clearly written calculation. 3. Write both values with the same unit next to each other. 4. Finish with a sentence that answers the question asked.
AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.