# Functional Skills: Unit Conversions

## Functional Skills: Unit Conversions Revision

**Units**

All measurements need **units**, whether that’s length, weight or capacity. There are two main types of units, **metric **and **imperial**. You will also encounter other **units**. You will need to be able to convert between units to solve calculations.

**Common Units**

The table below shows some common metric and imperial **units** for length, weight and capacity. The length of something is how long it is. The weight of something is how heavy it is. The capacity of something is how much it can hold.

**Metric and Imperial Unit Conversions**

You will need to know the **conversion factor** to go between **metric **and **imperial **units, to then multiply or divide by this value to convert the unit.

The tables below show some common **metric **and **imperial **unit conversions. You only need to memorise the **metric **conversions, if you have to convert **imperial **units you’ll be told the **conversion factor.**

You can convert between **any** units as long as you are given (or know) the **conversion factor**.

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**Unit Conversions – Metric and Money**

Converting **Metric **units is very simple, all we need to do is multiply or divide similar units by a **conversion factor**.

**Example:** Converting from \text{kg} to \text{g} and vice versa:

3\text{ kg} = 3 \times 1000 = 3000\text{ g}

3000\text{ g} = 3000\div 1000 = 3\text{ kg}

**Example:Â **Converting from Pounds (Â£) to pence (p) and vice versa:

Â£3.50 = 3.5 \times 100 = 350p

350p = 350\div 100 = Â£3.50

**Unit Conversions – Volume**

There are different ways the units of volume can be written:

\begin{aligned} \textcolor{red}{1 \text{ cm}^3} &= \textcolor{red}{1 \text{ ml}} \\ \textcolor{blue}{1 \text{ m}^3} &= \textcolor{blue}{1000 \text{ L}} \end{aligned}

You may be given questions where you have to convert between these, but you will be given these in the question.

**Example 1: Metric to Imperial Conversion**

Frazer buys a bag of soil for his garden that has a mass of 15.2 kg. What is the mass of the bag of soil in pounds to 1 decimal place?

Use the conversion rate 1 pound = 0.4536\text{ kg}.

**[2 marks]**

To convert from kilograms to pounds we need to divide by 0.4536

\text{Mass of bag of soil} = 15.2\div 0.4536 = 33.5 pounds (1 decimal place)

**Example 2: Money Conversion**

Sanjay paid \$400 for a hotel stay. How much is this in pounds (Â£)?

Â£1 = \$1.25**[1 mark]**

400 \div 1.25= 320

So, Sanjay paid Â£320 for the hotel stay.

**Example 3: Volume Conversion**

Shavaughn has a measuring cylinder with a capacity of 250 cm^3. She pours water into the cylinder, and stops when the water takes up half of the measuring cylinder’s capacity.

What volume of water did Shavaughn pour into the measuring cylinder? Give your answer in millilitres.

Use 1 cm^3 =1 ml

**[2 marks]**

250 \div 2=125 cm^3

125 cm^3 = 125 ml

## Functional Skills: Unit Conversions Example Questions

**Question 1:** Kerry is going on holiday to Spain and needs to convert Â£400 into euros. There is a 2\% fee for converting the currency.

Using the conversion rate: \pounds 1 = â‚¬1.17, calculate how many euros she will be able to take on holiday.

**[2 marks]**

We can either deduct the 2\% commission from the amount in pounds at the start or from the amount in euros at the end.

A 2\% decrease means she will have 98\% of her money left over, so

\text{Money left } = \dfrac{98}{100} \times 400 = \pounds 392

Using the conversion rate given in the question, we can find out how much Â£392 is in euros.

392\times 1.17 = â‚¬458.64

**Question 2:** Meghan goes on a 3.1 kilometre walk with her dog. What is the distance of Meghan’s walk in feet, to the nearest foot?

Use the conversion rate: 1\text{ foot} = 0.3048\text{ metres}.

**[2 marks]**

The conversion rate is between metres and feet, so first we need to convert 3.1km into metres. We know that 1km is 1000m, so:

3.1\text{km} = 3.1 \times 1000 \text{m} = 3100\text{m}

If 1 foot is equal to 0.3048 metres, that means we would have to multiply a distance in feet by 0.3048 in order to get the equivalent distance in metres. So, to go from metres to feet, we will have to divide by 0.3048. This means Meghan’s walk in feet is:

3100 \text{ metres} \div 0.3048 \text{ metres}= 10171\text{ feet} Â (to nearest foot)}

**Question 3: **Declan has bought a container that measures 90\text{ cm} \times 130\text{ cm} \times 110\text{ cm}. What is the volume of his container in litres?

1 m^3 = 1000 L

**[3 marks]**

Converting the measurements from cm to m first:

90 cm = 0.9 m

130 cm = 1.3 m

110 cm = 1.1 m

Then calculate the volume of the container in m^3:

0.9\times1.3\times1.1=1.287 m^3

Finally, convert to litres:

1.287 m^3 = 1287 L

**Question 4:**Â A runner runs at an average pace of 6 minutes and 12 seconds per kilometre during a 10 mile race. Calculate how long will it take the runner to complete the race.Â Give your answer in hours and minutes, rounding your answer to the nearest minute.

Use the conversion rate: 1 \text{ mile} = 1.61 \text{ kilometres}

**[3 marks]**

We first need to convert the distance of the race from miles to kilometres, as the average pace has been given in minutes per kilometre. We can convert 10 miles into kilometres as follows:

10 \text{ miles} \times 1.61 \text{ kilometres} = 16.1\text{ kilometres}

If it takes the runner 6 minutes and 12 seconds to run one kilometre, then we simply need to multiply 16.1 kilometres by the runnerâ€™s pace.

6 \text{ minutes } 12 \text{ seconds} \equiv 6.2 \text{ minutes}

(Remember that 12 seconds is \frac{1}{5} a minute = 0.2 minutes)

The total time to complete the 10 mile race at a pace of 6.2 minutes per kilometre is therefore:

16.1\text{ kilometres} \times 6.2\text{ minutes per kilometre} = 99.82\text{ minutes}

The question says that we can round the answer to the nearest minute, so the half marathon will take 100 minutes, which is 1 hour and 40 minutes.

**Question 5:** In January a businessman buys Â£3500 of dollars. He then trades back to pounds in February.Â To the nearest pound, what profit has the businessman made?

January exchange rate: \pounds1 = \$1.40

February exchange rate: \pounds1 = \$1.37

**[2 marks]**

If the businessman exchanges Â£3500 into dollars in January, we need to calculate how many dollars he receives. If Â£1 equates to \$1.40, then Â£3500 can be converted as follows:

\pounds 3500 \times \$1.40= \$4900

If he trades the \$4900 back into pounds in February, we need to calculate how many pounds he will receive. The exchange rate is \$1.37 to the pound, so we need to see how many times \$1.37 goes into \$4900:

\$4900\div \$1.37= \pounds 3577 (to the nearest pound).

If the businessman started with Â£3500 and ended up with Â£3577, he has made a profit of Â£77.

## Functional Skills: Unit Conversions Worksheet and Example Questions

### Unit Conversions L2

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