Convert rates
Converting rates allows us to compare rates given in different units and to also obtain a rate in unit suitable for a particular application.
To convert a rate, we want to multiply or divide the rate by the appropriate constant. So to convert a rate in m/min to m/s, we want to divide the rate by $60$60. This is because a rate given in m/min, tells us the number of metres per minute, which is the number of metres per $60$60 seconds.
Worked examples
Example 1
Convert the rate of $20$20 L/h to a rate in L/min.
Think: We first need to identify which unit we are changing. Is it the first unit, the second unit or are we converting both? In this case, we are only changing time from hours to minutes. We also need to identify what the conversion factor between these units is. In our case, $1$1 hour is equivalent to $60$60 minutes.
Do: The number of litres in an hour must be $60$60 times more than the number of litres in a minute. So we want to divide the given rate by $60$60.
| Rate | $=$= | $20$20 L/h |
Write the rate as a division including units. |
| $=$= | $\frac{20}{60}$2060 L/min |
Convert hours to minutes by dividing by $60$60. |
|
| $=$= | $\frac{1}{3}$13 L/min |
Simplify the fraction if possible. |
Example 2
How fast is Usain Bolt's world record speed of $12.2$12.2 m/s in km/h?
Think: Both the distance unit and time unit are being converted. Let's first change the distance unit. In this case, we are changing distance from metres to kilometres. The number of metres travelled in a given second is $1000$1000 times greater than the number of kilometres, so we want to divide the rate by $1000$1000.
Then we want to convert the new rate in km/s to km/h. There are $60$60 seconds in a minute, and then $60$60 minutes in an hour, so the number of kilometres travelled in an hour will be the rate in km/s multiplied by $60^2$602.
Do:
| Rate | $=$= | $12.2$12.2 m/s |
Write the rate as a fraction including units. |
| $=$= | $12.2/1000$12.2/1000 km/s |
Convert metres to kilometres by dividing by $1000$1000. |
|
| $=$= | $0.0122$0.0122 km/s |
Simplify the rate. |
|
| $=$= | $0.0122\times60^2$0.0122×602 km/h |
Convert seconds to hours by multiplying by $60^2$602. |
|
| $=$= | $43.92$43.92 km/h |
Simplify the rate. |
Reflect: Alternatively, we can convert km/s to km/h by converting in stages. First we can find the rate in km/m, by multiplying by $60$60 and then we can find the rate in km/h by multiplying by $60$60 again.
When converting units think carefully about if your answer should get smaller or larger and, if you need to divide or multiply by the conversion factor. For instance, the distance you travel in metres in an hour, should be greater than the number of kilometres travelled in an hour. So a rate in m/h should be greater if it was given in km/h.
$\text{1 metre}=\text{100 centimetres}$1 metre=100 centimetres
$\text{1 metre}=\text{1000 millimetres}$1 metre=1000 millimetres
$\text{1 kilometre}=\text{1000 metres}$1 kilometre=1000 metres
$\text{1 litre}=\text{1000 millilitres}$1 litre=1000 millilitres
$\text{1 hour}=\text{60 minutes}$1 hour=60 minutes
$\text{1 minute}=\text{60 seconds}$1 minute=60 seconds
Practice questions
Question 1
Convert $96$96 L/day to L/h.