Our second skill to review from Chapter 2 is writing one amount as a percentage of another.
To express one quantity as a percentage of another, first write the first quantity as a fraction of the second and then multiply by $100%$100%.
Worked example
A car has a fuel tank with a capacity of $40$40L but which currently only has $15$15L of fuel in it.
(a) What percentage full is the fuel tank?
Think: What would the fraction of fuel in the tank be? Remember that in a fraction the numerator will represent how much there is and the denominator will represent the total capacity. Then to find what percentage of fuel is in the tank we multiply by $100%$100%.
Do:
| Percentage full | $=$= | $\frac{15}{40}\times100%$1540×100% | |
| $=$= | $37.5%$37.5% |
Use calculator to simplify. |
(b) What percentage of the tank is empty?
Think: We can work this out as above knowing that the capacity that is not filled is $40$40L $-15$−15L $=25$=25L. Alternatively, as these are complementary events and add to $100%$100%, we can subtract our percentage found in part (a) from $100%$100%.
Do:
| Percentage empty | $=$= | $100%-37.5%$100%−37.5% |
| $=$= | $62.5%$62.5% |
When writing an amount as a percentage of another ensure all quantities are in the same units.
Practice questions
Question 1
There are $2$2 boys and $7$7 girls in a class.
Find the total number of students in the class.
What percentage of the class is boys?
Write your answer as a percentage correct to 2 decimal places.
What percentage of the class is girls?
Write your answer as a percentage correct to 2 decimal places.
Question 2
Luke buys a used bike for $\$485$$485 and resells it for $\$690$$690 without spending any money on it.
How much profit did Luke make on the bike?
Now express this profit as a percentage of the original price.
Make sure to give your answer as a percentage, rounding to two decimal places.
Question 3
What percentage is $385$385 metres of $4$4 km?
Question 4
A dishwasher weighs exactly $30.3$30.3 kg, but was measured by Luke to be $35$35 kg.
Determine the absolute difference of this measurement.
Now determine the relative error, as a percentage correct to one decimal place.