# 5.1 Converting between different unit systems

Many people find converting between units quite challenging at first – but the more you practise, the easier it will become. Hopefully, you are already finding this yourself. The process that you have been following has three steps:

- Find out how the two units are related to each other – the ‘conversion factor’.
- Ask yourself if the final answer should be bigger or smaller than the original value.
- Divide or multiply by the conversion factor to get your answer.

If you are lucky, and with practice, you may be able to miss step two out altogether – but that may depend on what you are trying to convert.

The process to use when converting between metric and imperial, or imperial and metric, is just the same as outlined above.

Let’s look at an example to see this approach in action.

## A man's height

A man measures 1.8 m and needs to know his height in feet and inches.

The first step is to find out how the units relate to each other. From the previous section, 1 m is the same as 39.4 inches.

This means that the answer in inches must be bigger than the original value, so multiply by 39.4. So, the

Now, this needs to be converted to feet and inches. There are 12 inches in 1 foot, so this time the conversion is from a physically smaller unit to a physically larger unit and the answer will be smaller. So now divide by 12 to convert from inches to feet.

Now you know that 1.8 m is the same as 5.91 feet, which is 5 feet and 0.91 of a foot. However, the final answer should be in feet and inches, so now find out what 0.91 of a foot is in inches.

This is a conversion from a larger to a smaller unit, so multiply by the conversion factor in this case.

Putting this altogether, a man who is 1.8 m is about 5 feet 11 inches.

You can apply the same technique for any units, so see how you get on with these next activities. Take your time and think carefully about whether you need to divide or multiply.

## Activity 3 Converting length measurements between systems

- a.The distance between Fort William and Glasgow is about 108 miles. What is this distance in kilometres, to the nearest km? Click on ‘reveal comment’ if you feel you need more guidance.

### Comment

1 mile = 1.6 km

### Answer

You know that 1 mile = 1.6 km

This means converting from a physically larger unit to a smaller one, so the expected converted answer will be larger. Hence, you need to multiply by the conversion factor.

So, the distance from Fort William to Glasgow is 173 km.

- b.The North Downs Way is a footpath in the South of England. The total length of the route is about 250 km. What is this distance in miles?

### Comment

1 mile = 1.6 km

### Answer

b.You know that 1 mile = 1.6 km

This means converting from a physically smaller unit to a bigger one, so the expected converted answer will be smaller. Hence, you need to divide by the conversion factor.

So, the North Downs Way is 156 miles long.

- c.A reel of thread contains 182 yards of cotton. How long is the thread in metres, to the nearest metre?

### Comment

1 yard = 0.9 metres

### Answer

c.You know that 1 yard = 0.9 metres

This means converting from a physically smaller unit to a larger one. However, the conversion factor is less than one so the expected converted answer will be larger. Hence, you need to multiply by the conversion factor.

So, the reel has 164 metres of cotton on it.

You’ve got one final activity to look at before finishing this week. This brings together your new conversion skills, as well as giving you a refresher on problem solving from *Succeed with maths – Part 1* [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .