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

A compound measure is often one unit divided by another (sometimes it can be one unit multiplied by another). Velocity is given as metres per second, which can be written as either `frac(m)(s)` or as ms^{-1} (the -1 shows that the seconds are dividing.

The compound measure can include square or cube terms. Density is weight per unit of volume, so it may be written as, for example, kg/m^{3} or kg m^{-3}.

When converting compound measures, all of the units have to be considered. For example, converting kilometres per hour (km/h) to metres per second (m/s) needs the conversion of both unit types.

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

The measure is 50 kilometres in 1 hour.

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}.

Answer: 13.9ms^{-1}

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?

Density is given by weight ÷ volume.

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

Answer: Yes

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