Metric units convert by multiplying or dividing by 10, 100 or 1000: 1 m = 100 cm, 1 kg = 1000 g and 1 litre = 1000 ml. Multiply when changing to a smaller unit and divide when changing to a larger one. Time is different, because it works in sixties: 60 seconds in a minute and 60 minutes in an hour.
Metric units
- Length: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m
- Mass: 1 g = 1000 mg, 1 kg = 1000 g, 1 tonne = 1000 kg
- Capacity: 1 l = 1000 ml, 1 l = 100 cl, 1 cm³ = 1 ml
- Time: 60 s = 1 min, 60 min = 1 h, 24 h = 1 day
Converting to a smaller unit: multiply. Converting to a larger unit: divide.
Converting metric units
Metric units are based on powers of 10. To change to a smaller unit, multiply, because you need more of the smaller units: 3.5 m = 3.5 × 100 = 350 cm. To change to a larger unit, divide: 2750 g = 2750 ÷ 1000 = 2.75 kg.
Choosing sensible units
Choose a unit that suits the size of the thing being measured: millimetres for the thickness of a coin, metres for the length of a room and kilometres for a journey; grams for an apple, kilograms for a person and tonnes for a lorry. Exam questions sometimes ask you to pick or estimate a sensible measurement.
Comparing and calculating with measures
Always convert to the same unit before comparing or calculating. To compare 0.5 kg with 400 g, write 0.5 kg as 500 g. In a problem such as filling cups from a jug, convert both to millilitres first, then divide, and round to a sensible answer for the context.
Time and the 24-hour clock
Time does not work in tens: there are 60 seconds in a minute and 60 minutes in an hour. So 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes. The 24-hour clock avoids am and pm: add 12 to afternoon times, so 4:15 pm is 16:15.
Calculating durations
To find the time between two times, count on in stages: to the next full hour, then the whole hours, then the remaining minutes. From 09:45 to 13:20 is 15 minutes, then 3 hours, then 20 minutes: 3 hours 35 minutes.
Worked examples
Example 1. Convert 3.5 m to centimetres.
- 1 m = 100 cm, and centimetres are smaller, so multiply.
- 3.5 × 100.
Answer: 350 cm.
Example 2. Which is heavier: 0.5 kg or 400 g?
- Convert to the same unit: 0.5 kg = 500 g.
- 500 g is more than 400 g.
Answer: 0.5 kg is heavier.
Example 3. Convert 2750 g to kilograms.
- 1 kg = 1000 g, and kilograms are larger, so divide.
- 2750 ÷ 1000.
Answer: 2.75 kg.
Example 4. A bottle holds 1.2 litres. How many 150 ml glasses can be filled from it?
- Convert: 1.2 litres = 1200 ml.
- 1200 ÷ 150.
Answer: 8 glasses.
Example 5. A train leaves at 09:45 and arrives at 13:20. How long is the journey?
- 09:45 to 10:00 is 15 minutes.
- 10:00 to 13:00 is 3 hours; 13:00 to 13:20 is 20 minutes.
Answer: 3 hours 35 minutes.
Common mistakes
- Dividing when you should multiply. Changing to a smaller unit needs more of them, so multiply.
- Using 100 for every conversion. 1 km = 1000 m and 1 kg = 1000 g, but 1 m = 100 cm.
- Treating time as decimal. 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes.
- Comparing different units directly. Convert both measurements to the same unit first.
- Unrealistic answers in context. You cannot fill part of a glass in a “how many full glasses” question.
How units and measures are examined
Units and measures appear throughout Foundation papers for GCSE (1MA1) and in the 4MA1 International GCSE, often inside problems on area, speed or money. You will be asked to:
- convert between metric units of length, mass and capacity
- choose or estimate a sensible unit or measurement
- solve a problem that needs a conversion first
- calculate with time, durations and timetables
There is a converting units worksheet with answers, and the GCSE number revision engine for extra practice.
Unit conversions are used in converting compound units and speed, distance and time.
Frequently asked questions
How many centimetres are in a metre?
100.
How do you convert grams to kilograms?
Divide by 1000. For example, 3200 g = 3.2 kg.
What is 5:20 pm in the 24-hour clock?
17:20. Add 12 to the hours for afternoon times.