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Compound units are units that are made up of more than 1 unit. For example Speed (made up of distance and time), Density (Mass and Volume) and Pressure (Force and Area) are all examples of compound units.

While technically we have to be able to convert any of these, in practice you will probably only have to convert speed. If you get asked to convert one of the others, just follow the concepts here and you shouldn't go far wrong.

The one thing you need to know when you are converting compound units is that you have to do two steps.  To do this, I think the easiest method is to use proportional change.

Example 1: Change 10m/s into km/hr

Step 1: 10 m/s means '10 metres in 1 second. Write this out as a proportion.

10 metres = 1 second

Step 2: Change the time units.

It's easier to change the seconds into hours first. 1 hr = 3600 seconds, so we can multiply both sides by 3600 to get.

36000 metres = 3600 seconds

36000 metres = 1 hour

Step 3: Convert the other unit

We know that 1 km = 1000 m, so we can now change the distance travelled into kilometres

36 km = 1 hour

Since we now have our units as kilometres and hours, we can say that 10m/s = 36 km/hr

Example 2: Change 20 km/hr into m/s

Step 1: 20km/hr means '20 likometres in 1 hour. Write this out as a proportion.

20 kilometres = 1 hour

Step 2: Convert the units into metres and seconds.

We know that 1 hr = 3600 seconds and 1km = 1000, so we can convert both sides into the other units

20 kilometres = 1 hour

20000 m = 3600 seconds

Step 3: Change the time to 1

We currently have how many metres we travel in 3600 seconds, but we want to know how many we travel in 1 second. To get this, we divide both sides by 3600

5.56 m = 1 second

Since we now have our units as metres and seconds, we can say that 20km/hr = 5.56 m/s

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