# Conversions Worksheets, Questions and Revision

GCSE 4 - 5KS3AQAEdexcelOCRWJECAQA 2022Edexcel 2022WJEC 2022

## Conversions

A unit is a standard measurement of a particular quantity. For example, metres and kilometres are both units for measuring distance, and seconds, minutes, and hours are all units for measuring time. You will need to be familiar with Metric and Imperial unit conversions, which are two main types of unit.

## Important Note:

You will also need to know how to write different units. For example, one unit of speed is “metres per second” (written like $\text{m/s}$ or $\text{ms}^{-1}$), and one unit for density is “grams per cubic metre” (written like $\text{g/m}^3$ or $\text{gm}^{-3}$). “Per” means that we divide the first unit by the second.

These kinds of units that contain more than one type of unit are called compound units.

Level 1-3 GCSE KS3

## Metric and Imperial Unit Conversions

The tables below show some common Metric and Imperial unit conversions. You only need to memorise the Metric conversions. For GCSE Maths, all Imperial or Metric-Imperial conversions will be given.

Level 1-3GCSEKS3

## Converting Units – Metric and Money

When converting Metric units, all we need to do is multiply or divide similar units by a scale factor.

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

$4\text{kg} = 4 \times 1000\text{g} = 4000\text{g}$

$4000\text{g} = 4000\text{g} \div 1000\text{g} = 4\text{kg}$

Example: Converting money for example Pounds (£) to pence (p) and vice versa

$£4 = 4 \times 100 = 400p$

$400p = 400 \div 100 = £4$

These are as simple as conversions go, we will see that conversions can get a lot harder.

Level 1-3GCSEKS3
Level 4-5 GCSE KS3

## Converting Units – Time and Speed

Time conversions are harder than what we have previously seen. Time units are not in multiples of $10$ or $1000$ etc, so we have to think a bit more.

Speed conversions are some of the most difficult conversions you will see. This is because they are made up of two different measures. We have to convert the distance units and time units one at a time.

Example: A car is driving at $\textcolor{red}{50}$ $\text{km/h}$. Give the speed of the car in metres per second.

Step 1: Convert the distance

$1 \, \text{km} = 1000 \, \text{m}$

$\textcolor{red}{50} \, \text{km}= 50 \times 1000 = \textcolor{blue}{50000}\, \text{m}$

So, the speed of the car is $50000$ metres per hour.

Step 2: Convert the Time

$1 \, \text{minute} = 60 \, \text{seconds}$

$1 \, \text{hour} = 60 \, \text{minutes}$

$1 \, \text{hour} = 60 \times 60 = \textcolor{limegreen}{3600} \, \text{seconds}$

Step 3: Divide Distance by time

In other words, it will take this particular car $\textcolor{limegreen}{3600}$ seconds to travel $\textcolor{blue}{50000}$ metres, so the number of metres they travel every second will be:

$\textcolor{blue}{50000} \div \textcolor{limegreen}{3600} = \textcolor{orange}{13.9}$ ($1$ dp).

Thus, the speed of the car is $\textcolor{orange}{13.9}$ metres per second.

Level 4-5GCSEKS3
Level 4-5 GCSE KS3

## Converting Units – Length, Area, Volume (Metric)

From the red Metric conversions table, we can see that there are three different length unit conversions we need to know, $\text{\textcolor{red}{mm}}$ to $\text{\textcolor{blue}{cm}}$ to $\text{\textcolor{limegreen}{m}}$ to $\text{\textcolor{purple}{km}}$ and vice versa.

When converting areas from one unit to another, we need to be careful, as we are multiplying two units together.

$1\text{ m}^2 = 100\text{\textcolor{blue}{ cm}} \times 100\text{\textcolor{blue}{ cm}} = 10000 \text{ cm}^2$

$1\text{ cm}^2 = 10\text{\textcolor{red}{ mm}} \times 10\text{\textcolor{red}{ mm}} = 100 \text{ mm}^2$

Do not do this $\xcancel{1\text{ m}^2 = 100\text{ cm}^2}$!

Converting volumes from one unit to another is similar to areas, but now there is another multiplication involved.

$1\text{ m}^3 = 100\text{\textcolor{blue}{ cm}} \times 100\text{\textcolor{blue}{ cm}} \times 100\text{\textcolor{blue}{ cm}} = 1000000 \text{ cm}^3$

$1\text{ cm}^3 = 10\text{\textcolor{red}{ mm}} \times 10\text{\textcolor{red}{ mm}} \times 10\text{\textcolor{red}{ mm}} = 1000 \text{ mm}^3$

Level 4-5GCSEKS3
Level 4-5 GCSE KS3

## Example 1: Metric to Imperial Conversion

A baby is born weighing $4.2$ kg. What is the mass of the baby in pounds to $3$ sf?

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

[2 marks]

We have to convert a value from kilograms into pounds. That conversion rate tells us that to get from pounds to kilograms, we would need to multiply by $0.4536$. Therefore, in order for us to convert kilograms to pounds we must do the opposite and divide by $0.4536$.

$\text{Mass of baby } = 4.2 \div 0.4536 = 9.26$ pounds ($3$ sf)

Level 1-3 GCSE KS3

## Example 2: Volume Conversion

Shape A has a volume of $2.5$ m$^3$ . What is this volume in cm$^3$?

[1 mark]

$2.5$ m$^3 = 2.5 \times 1$ m$^3 = 2.5 \times 1000000$ cm$^3 = 2500000$ cm$^3$

Level 4-5GCSEKS3

## Example Questions

We can either deduct the $3\%$ commission from the amount in pounds at the start or from the amount in dollars at the end (it won’t make a difference); I’d recommend getting it out of the way now. A $3\%$ decrease means she will have $97\%$ of her money left over, so

$\text{Money left } = \dfrac{97}{100} \times 500 = \pounds 485$

If $£1$ is worth $\1.56$ dollars, and we are converting $£485$, this means that we are converting $485$ times the number of pounds given to us in the exchange rate.  This means that she will receive $485$ times the dollar figure from the exchange rate.  Therefore, the number of dollars she receives is:

$485 \times 1.56 = \756.60$

The conversion rate is between metres and feet, so first we need to convert $2.3$km into metres. We know that $1$km is $1000$m, so:

$2.3\text{km} = 2.3 \times 1,000 \text{m} = 2,300\text{m}$

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 Diana’s walk in feet is:

$2,300 \text{ metres} \div 0.3048 \text{ metres}= 7,546 \text{ feet}$  (to nearest foot)}

The volume of his fish tank in $\text{cm}^3$ is:

$120 \text{ cm} \times 180 \text{ cm} \times 100 \text{ cm} = 2160000 \text{ cm}^3$

We know that

$1 \text{ m}^3 = 1000000 \text{ cm}^3$

So the volume of his fish tank in $\text{m}^3$ is:

$2160000 \div 1000000 = 2.16 \text{ m}^3$

Since we have been given a pace in minutes per kilometre, we will need to convert the race distance of $13.1$ miles into kilometres.  We can convert $13.1$ miles into kilometres as follows:

$13.1 \text{ miles} \times 1.61 \text{ kilometres} = 21.091 \text{ kilometres}$

If it takes the runner $5$ minutes and $30$ seconds to run one kilometre, then we simply need to multiply $21.091$ kilometres by the runner’s pace.  However, the pace of the runner is in mixed units, so we will need to convert it.  It makes sense to keep the pace in minutes rather than convert to seconds per kilometre:

$5 \text{ minutes } 30 \text{ seconds} \equiv 5.5 \text{ minutes}$

(Remember that 30 seconds is $\frac{1}{2}$ a minute = $0.5$ minutes)

The total time to complete the half marathon at a pace of $5.5$ minutes per kilometre is therefore:

$21.091 \text{ kilometres} \times 5.5 \text{ minutes per kilometre} = 116.0005 \text{ minutes}$

The question says that we can round the answer to the nearest minute, so the half marathon will take $116$ minutes.

We now need to convert $116$ minutes into hours and minutes:

$116 \text{ minutes} \equiv 1 \text{ hour } 56 \text{ minutes}$

If the businessman exchanges $£5,000$ into euros in January, we need to calculate how many euros he receives.  If $£1$ equates to €$1.16$, then $£5,000$ can be converted as follows:

$\pounds5,000 \times €1.16 = €5,800$

If he trades the €$5,800$ back into pounds in February, we need to calculate how many pounds he will receive.  The exchange rate is €$1.15$ to the pound, so we need to see how many times €$1.15$ goes into €$5,800$:

$€5,800 \div €1.15 = \pounds5,043$ (to the nearest pound).

If the businessman started with $£5,000$ and ended up with $£5043$, he has made a profit of $£43$.

## Worksheet and Example Questions

### (NEW) Conversions Exam Style Solutions - MME

Level 4-5 GCSENewOfficial MME

### (NEW) Unit Conversions Exam Style Solutions - MME

Level 1-3 GCSENewOfficial MME

Level 1-3 GCSE

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