Conversion Graphs Worksheets | Questions and Revision | MME

Conversion Graphs Worksheets, Questions and Revision

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What you need to know

Conversion Graphs

A conversion graph is a tool that we use to convert between different units. Any conversion graph you see will be a straight-line graph. You have to know how to construct a conversion graph given a conversion rate, and also how to use a conversion graph. To learn more about unit conversions and metric and imperial units, head over to our dedicated conversions revision page first.

Example 1: Conversion Graphs

Shown is a conversion graph for converting between litres and fluid ounces.

Using the graph, convert

i) 2.5 litres to fluid ounces;

ii) 24 fluid ounces to litres.

As we can see, the graph shown has litres on the y-axis and fluid ounces on the x-axis. When using these kinds of graphs, always be wary of the scales on both axes.

So, in order to use the graph to convert the values given, we need to draw on the graph. To do this (in this case to find a conversion for 3 litres) we do the following:

1.Starting from 3 on the y-axis, draw a horizontal line until you meet the graph (the blue line).

2.From the point where your line meets the graph, draw a vertical line down until it meets the x-axis.

3.Read the value where your line met the x-axis – trying to be as accurate as possible – and you have the result of the conversion.

Then, when we have to convert in the other direction, we simply reverse the process: draw up to the graph first, then across, and this time read the result off the y-axis. For both conversions, i) and ii), the graph would look like this:

i) We can see that the 2.5-litre line ends up at 88 on the x-axis, so we get

$\mathbf{2.5 \text{ litres }=88\text{ fluid ounces}}$

ii) We can also see that the 24-fluid-ounce line ends up between 0.6 and 0.8 on the y-axis. It looks to be about halfway between the two small squares, so it’s safe to go for 0.7. So, we get

$\mathbf{24 \text{ fluid ounces }\equiv 0.7 \text{ litres }}$

Example 2: Conversion Graphs

a) Draw a conversion graph for ‘miles per hour’ and ‘metres per second’ using the conversion rate below.

$1\text{ mile per hour }\equiv 0.447\text{ metres per second }$

b) Use your conversion graph to convert 1.5 m/s into m/h.

To draw a straight-line graph that represents this conversion, we need some points to plot. We will assume here that the axes are given with m/h on the x-axis whilst m/s on the y-axis.

We know that 1 m/h is the same as 0.447 m/s. This means that the line on our conversion graph must pass through the coordinate (1, 0.447) – this is our first point. To find others, think of the conversion as a ratio. The ratio of “m/h : m/s” is “1 : 0.447”. Now, a ratio can be scaled up, i.e. we can times both values by the same number without changing it. Multiplying both parts by 2 we get

$1 : 0.447 = 2 : 0.894$

This means we have a second coordinate that the line must pass through: (2, 0.894). Lastly, if we multiply both values in the ratio by 2 again, we get

$2 : 0.894 = 4 : 1.788$

So, our third coordinate is (4, 1.788). Now, we must plot these three points and draw the most accurate straight line through them that we can. The result should look like the graph shown here.

Now we’ve got the graph we can use it!

b) Drawing a line across for 1.5 on the ‘metres per second’ axis and following the process for using a conversion graph should look like the graph shown below.

Example Questions

a) since we are converting litres to pints, we need to locate the value 3 on the horizontal (x) axis and draw a line vertically upwards until it touches the blue line of the graph. Then we need to draw a line from this point horizontally to the left to find the corresponding value on the vertical (y) axis. This value falls between 5.2 and 5.4 pints, so the approximate answer is 5.3 pints.

b) since we are converting pints to litres, we need to locate 3.8 on the vertical (y) axis and draw a line horizontally to the right until it touches the blue line of the graph. Then we need to draw a line from this point vertically down to find the corresponding value on the horizontal (x) axis. This value falls between 2 and 2.2 litres. Since it is closer to 2.2 than 2, the approximate answer is 2.15 litres.

a) We know that 1 inch equals 2.54 cm, so we can plot the point $(1, 2.54)$ on the graph.

If 1 inch equals 2.54 cm, then the cm equivalent of 3 inches can be calculated as follows:

$3\text{ inches}\times 2.54 \text{ cm} = 7.62 \text{ cm}$

As a result, we can now plot the point $(3, 7.62)$ on the graph.

If 1 inch equals 2.54 cm, then the cm equivalent of 6 inches can be calculated as follows:

$6\text{ inches}\times 2.54 \text{ cm} = 15.24 \text{ cm}$

As a result, we can now plot the point $(6, 15.24)$ on the graph.

Now all we need to do is join the points, as per the graph below.

(We could have skipped one of the steps above as you only need to work out two points in order to draw a straight line, although 3 points does ensure that you haven’t made an error. If you have plotted 3 points and they are not in line, then one of your points has been calculated incorrectly.)

b) To use this graph to convert 10cm to inches, we must locate 10cm on the vertical (y) axis and draw a horizontal line to the right until it touches the line of the graph. We then draw line vertically down to find the corresponding value on the horizontal (x) axis. The value on the x axis is halfway between 3.8 and 4, so 10 cm is the equivalent of 3.9 inches.

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