GCSE(F),

**Compound measures** all involve measuring using more than one type of measurement.

An example of a compound measure is the speed of a car, which might be given in metres per second. This speed is the number of metres travelled in one second. So a speed of 8 metres per second is 8 metres travelled for each 1 second. The units are also divided: `frac(m)(s)`, and will be written either as m/s or as 8ms^{-1} (the -1 suffix shows that the seconds are a divisor).

Density is another compound measure in common use. Density is the amount of something in something else: For example, population density is the number of people in an area: for example, 46.55 people / km^{2} or 46.55 people km^{-2}. In science, engineering and other areas, **density** may refer to a gas, liquid or solid, and is the amount of mass for a unit of volume.

1. A car is travelling at 50 kilometres per hour. What is the speed of the car in metres per second?

Answer: 13.9ms^{-1}

Change the kilometres to metres: 50 x 1000 = 50 000m.

Change the time from hours to minutes: 1 hour = 60 x 60 = 3600 seconds.

Calculate `frac(50 000)(3 600)` = `frac(500)(36)` = 13.9ms^{-1}.

2. A jeweller has been asked to prove whether a bracelet is fake. He knows that gold should have a density of 19.3g cm^{-3}. The weight of the bracelet is 96g. The volume of the bracelet is 6.2cm^{3}. Is it fake?

Answer: Yes

The density of the bracelet is 96 รท 6.2 = 15.48g cm^{-3}. It is fake.

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