# Convert Compound Units

In this worksheet, students practise converting units of speed.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Mensuration

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Units and Measurement

Difficulty level:

### QUESTION 1 of 10

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

If I travel 20 metres in 1 second, how many metres will I travel in 1 hour?  Give your answer as a number, you do not need to give units in your answer.

I travel 7500 km in 1 hour, how many metres have I travelled in this time?

Complete the following sentence.

(All the answers should be given as numbers)

Complete the following sentence.

All the answers should be given as numbers.

25 m/s in km/hr is...

90 km/hr

6.95 km/hr

Which of the following answers is correct when you convert 12k m/hr to m/s?

43.2 m/s

3.34 m/s

Match the converted units.

## Column B

10 m/s
15.56 m/s
14m/s
6.1 m/s
22 km/hr
50.4 km/hr
56 km/hr
36 km/hr

To convert m/s into km/hr, do we...

x 3600 then ÷ 1000

÷ 1000 then x 3600

Either, it doesn't matter

Change 32 m/s into km/hr

Don't worry about the units, just put in the number.

Change 42 km/hr into m/s

Don't worry about the units, just put in the number. Give your answer to 2 decimal place

• Question 1

If I travel 20 metres in 1 second, how many metres will I travel in 1 hour?  Give your answer as a number, you do not need to give units in your answer.

72000
EDDIE SAYS
This question asks for the answer in metres, so we don't need to change the distance units. There are 3600 seconds in 1 hour, so all we have to do is multiply by 3600.
• Question 2

I travel 7500 km in 1 hour, how many metres have I travelled in this time?

0.75
0.75m
0.75 m
EDDIE SAYS
Once again, we aren't changing the time so we just have to convert the distance to km. If there are 1000 m in 1 km, we just need to divide,
• Question 3

Complete the following sentence.

(All the answers should be given as numbers)

EDDIE SAYS
As we discussed in the intro, the first step is to convert the time which has a scale factor of 3600 and then the distance, which has a scale factor of 1000.
• Question 4

Complete the following sentence.

All the answers should be given as numbers.

EDDIE SAYS
It's just the other way round. Remember to convert the distance units first (1000) and then the time (3600)
• Question 5

25 m/s in km/hr is...

90 km/hr
EDDIE SAYS
Remember, m/s to km/hr is x 3600 then ÷ 1000
• Question 6

Which of the following answers is correct when you convert 12k m/hr to m/s?

3.34 m/s
EDDIE SAYS
Remember, m/s to km/hr is x 1000 then ÷ 3600
• Question 7

Match the converted units.

## Column B

10 m/s
36 km/hr
14m/s
50.4 km/hr
22 km/hr
6.1 m/s
56 km/hr
15.56 m/s
EDDIE SAYS
Do you even need to do the conversions here? We know that the m/s match with the km/hr (and vice versa). We can then just say that the slowest speed in m/s is the slowest speed in km/hr
• Question 8

To convert m/s into km/hr, do we...

Either, it doesn't matter
EDDIE SAYS
It doesn't matter. You can do it any order you want. The reason we normally multiply first is so we don't have to deal with decimals but you will get the same answer.
• Question 9

Change 32 m/s into km/hr

Don't worry about the units, just put in the number.

EDDIE SAYS
Just follow those nice simple rules. X 3600 then ÷ 1000
• Question 10

Change 42 km/hr into m/s

Don't worry about the units, just put in the number. Give your answer to 2 decimal place

11.67
EDDIE SAYS
Just follow those nice simple rules. X 1000 then ÷ 3600 I hope you noticed that there was a recurring decimal. The answer is 11.67 not 11.66 as you have to round up.
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