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4.10 A) Unit Conversion – Part 1

4.10 A) Unit Conversion – Part 1

We use standard units every day in real life to measure a variety of different quantities.

For example:

The units listed above are not the only units that are used to measure the different quantities.

We are usually given unit conversions in the form of:

For example:

- We can use seconds, minutes or hours to measure time
- We can use ml or litres to measure the volume of a liquid
- We can use grams, kilograms or tonnes to measure the mass of something
- We can use millimetres, centimetres or metres to measure length

The units listed above are not the only units that are used to measure the different quantities.

We are usually given unit conversions in the form of:

For example:

For unit conversions, there are two different ways that we can convert. We are going to go through these conversions for the first formula that we looked at. The formula is given below:

There are two different conversions that we can undertake:

Let’s use our centimetre and millimetre example:

- If we are converting the units from the unit that is 1 to the n unit, we multiply by n
- If we are converting the units from the n unit to the unit that is 1, we divide by n

Let’s use our centimetre and millimetre example:

Here are the instructions for the two calculations:

We are now going to have a look at two examples using this conversion.

- If we are converting cm into mm (converting the unit that is 1 into the n unit), we multiply by 10.
- If we are converting mm into cm (converting the n unit into the unit that is 1), we divide by 10.

We are now going to have a look at two examples using this conversion.

**Example 1**

What is 12.3 cm in millimetres?

The quantity in the question is given in cm and we are asked to convert it into millimetres (mm). There are 10 mm in 1 cm. The unit conversion is shown below:

We are converting cm to mm (we are converting the unit that is 1 to the n unit), which means that we need to multiply by 10.

The length in mm is 123 mm.

**Example 2**

Convert 368 mm into centimetres.

The question is using centimetres and millimetres. The unit conversion is given below:

We are converting mm into centimetres (we are converting the n unit to the unit that is 1), which means that we divide by 10. The working is shown below.

The length in mm is 36.8 mm.

**Converting from Standard Units**

Here are some common unit conversions that you will come across in the exam:

- 10 cm = 10 mm
- 1 m = 100 cm
- 1 km = 1,000 m
- 1 litre = 1,000 ml
- 1 kg = 1,000 g

It is worth writing these down on a revision card.

**Example 3**

Convert 6.3 km into metres.

The question is asking us about kilometres and metres. There are 1,000 m in 1 kilometre; this gives us the following unit conversion:

We are converting km into metres (we are converting the unit that is 1 to the n unit), which means that we multiply by 1,000.

The length in metres is 6,300 metres.

**Example 4 – Weight**

Complete the following questions:

- Convert 5.6 kilograms into grams
- Convert 890 grams into kilograms

**Part 1**

The first part of the question asks us to convert 5.6 kilograms into grams. Before we are able to complete this question, we need to know the conversion. There are 1,000 grams in 1 kilogram. The easiest way to remember this is that “kilo” means 1,000. Therefore, a kilogram is 1,000 grams (this is also true for kilometre, which is 1,000 metres).

The conversion for kilograms and grams is:

We are converting kilograms into grams. This means that we are converting the unit that is 1 into the n unit. Therefore, we multiply by 1,000. The working is shown below:

Therefore, 5.6 kilograms is 5,600 grams.

The second part of the question asks us to convert 890 grams into kilograms. We will be using the same unit conversion as the previous question and this unit conversion is shown below:

**Part 2**The second part of the question asks us to convert 890 grams into kilograms. We will be using the same unit conversion as the previous question and this unit conversion is shown below:

We are converting grams into kilograms, which means that we are converting the n unit into the unit that is 1. Therefore, we divide by 1,000. The working is shown below:

Therefore, 890 grams is 0.89 kilograms.

**Example 5**

Complete the following questions:

- Convert 45.2 ml into litres
- Convert 36.1 litres into ml

**Part 1**

The first part of the question asks us to convert 45.2 ml into litres. Before we are able to do this, we need to know the conversion. There are 1,000 millilitres in 1 litre. This gives us the conversion below:

We are converting ml into litres, which means that we are converting the n unit into the unit that is 1. Therefore, we divide by 1,000. The working is shown below:

Therefore, 45.2 ml is 0.0452 litres.

**Part 2**

The second part of the question asks us to convert 36.1 litres into ml. The conversion for this question is shown below:We are converting litres into millilitres, which means that we are converting the unit that is 1 into the n unit. Therefore, we multiply by 1,000. The working is shown below:

Therefore, 36.1 litres is 36,100 ml.