# 1.1 Changing units

Sometimes you will need to change between millimetres and centimetres, or centimetres and metres. For example, you might need to do this if you were fitting a kitchen or measuring a piece of furniture.

The diagram below shows you how to convert between metric units if you’re calculating any of the following:

- length, which is a measurement of how long something is
- mass (sometimes referred to as weight), which is a measurement of how heavy something is
- volume (sometimes referred to as capacity), which is a measurement of how much space something takes up.

Starting with the smallest, metric measures of length are in millimetres, centimetres and metres. These three measurements are all related:

## Extract _unit3.1.1

10 millimetres (or mm, for short) = 1 centimetre (cm)

100 cm = 1 metre (m).

Please take a look at the example below on how to carry out simple metric conversions.

## Box _unit3.1.2

**Hint:** 10 millimetres = 1 centimetre, 100 centimetres = 1 metre

## Case study _unit3.1.1 Example: Making Christmas cards

You are making Christmas cards for a craft stall. You want to add a bow, which takes 10 cm of ribbon, to each card. You plan to make 50 cards. How many metres of ribbon do you need?

### Method

First you need to work out how many centimetres of ribbon you need:

- 10 × 50 = 500 cm

Notice that the question asks how many *metres* of ribbon you need, rather than centimetres. So you need to divide 500 cm by 100 to find out the answer in metres:

- 500 ÷ 100 = 5 m

Do you remember the metric conversion diagram at the start of this session?

Now try the following activity. Remember to check your answers once you have completed the questions.

## Activity _unit3.1.2 Activity 2: Measuring lengths

- You are fitting kitchen cabinets. The gap for the last cabinet is 80 cm. The sizes of the cabinets are shown in millimetres. Which size should you look for?
- Thirty children in a class each need 20 cm of string for a project. How many metres of string will they use all together?
- You want to buy 30 cm of fabric. The fabric is sold by the metre. What should you ask for?

### Answer

You will have found it useful to refer to the metric conversion diagram for this activity.

- To convert from centimetres to millimetres, you need to multiply the figure in centimetres by 10. The size is 80 cm, so the answer is:
- 80 × 10 = 800 mm

- Thirty children each need 20 cm of string. To find the total in centimetres you would do the following:
- 30 × 20 = 600 cm

However, the question asked for how much string is needed in

*metres*, not centimetres. To convert from centimetres to metres, you need to divide the figure in centimetres by 100. So if you need 600 cm, the answer is:- 600 ÷ 100 = 6 m

- To convert from centimetres to metres, you need to divide the figure in centimetres by 100. The length of fabric you need size is 30 cm, so the answer is:
- 30 ÷ 100 = 0.3 m

Now have a go at the following quickfire activity, using the conversion chart above if needed.

## Activity _unit3.1.3 Activity 3: Converting lengths

What are these lengths in another unit of measurement? Select the correct answers from the list of options below.

- 20 mm = ? cm

a.

200 cm

b.

2 cm

c.

0.2 cm

The correct answer is b.

- 450 mm = ? m

a.

45 m

b.

4.5 m

c.

0.45 m

The correct answer is c.

- 0.5 cm = ? mm

a.

5 mm

b.

15 mm

c.

50 mm

The correct answer is a.

- 400 cm = ? m

a.

0.4 m

b.

4 m

c.

40 m

The correct answer is b.

## Summary

In this section you have looked at measuring and calculating length. You have used different metric measurements, such as kilometres, metres and centimetres. You can now:

- measure and understand the sizes of objects
- understand different units of measurement.