Converting percentages and decimals
To convert a decimal to a percentage, multiply by $100%$100%. For example, $0.15$0.15 as a percentage or 'per $100$100' is $0.15\times100%=15%$0.15×100%=15%.
To convert a percentage to a decimal, divide by $100%$100%. For example, $212%=\frac{212%}{100%}=2.12$212%=212%100%=2.12
Practice questions
QUESTION 1
Convert $0.51$0.51 to a percentage.
Converting percentages and fractions
Given a percentage is out of $100$100, a percentage can be written as a fraction with a denominator of $100$100. To convert a percentage to a fraction, first write the percentage as the numerator, place $100$100 in the denominator and then simplify if possible.
For example, $28%=\frac{28}{100}$28%=28100 which simplifies to $\frac{7}{25}$725.
To convert from a fraction to a percentage, convert to a fraction with $100$100 as the denominator. For example, to write $\frac{4}{5}$45 as a percentage, multiply the top and bottom by $20$20.
$\frac{4}{5}=\frac{80}{100}$45=80100
$\frac{4}{5}=80%$45=80%
For fractions that do not convert nicely, you can convert the fraction to a decimal, then as seen in the section above, multiply by $100$100 to convert to a percentage. For example, to write $\frac{1}{3}$13 as a percentage, first convert to a decimal by dividing the numerator by the denominator to get $\frac{1}{3}=0.333\ldots$13=0.333…
Multiplying by $100$100 give $33.333\ldots$33.333… so $\frac{1}{3}=33.3\ldots%$13=33.3…% which can be expressed exactly as $33\frac{1}{3}%$3313% or approximately by $33.3%$33.3%
Practice questions
QUESTION 2
Convert $\frac{5}{10}$510 into a percentage.
Finding percentages of quantities
To calculate the percentage of a quantity, convert the percentage into a fraction or a decimal and then multiply by the quantity.
For example, to find $71%$71% of $526$526 L, multiply them together.
| $71%$71% of $526$526 | $=$= | $71%\times526$71%×526 |
| $=$= | $\frac{71}{100}\times526$71100×526 | |
| $=$= | $\frac{71\times526}{100}$71×526100 | |
| $=$= | $\frac{37346}{100}$37346100 | |
| $=$= | $\frac{18673}{50}$1867350 or $373.46$373.46 L |
One quantity as a percentage of another
We may need to express one amount as a percentage of another. For example we could express how full a water tank is by writing the current capacity as a percentage of the maximum capacity. For instance, a rainwater tank may currently contain $24$24 L of water in it but it can hold a maximum of $50$50 L.
To do this we write the two amounts as a fraction where the numerator represents the current amount and the denominator represents the maximum–which in this case, it's $\frac{24}{50}$2450. This question could also be asked as follows–what percentage is $24$24 of $50$50?
To convert it into a percentage we can use equivalent fractions to make the denominator $100$100:
$\frac{24}{50}=\frac{48}{100}$2450=48100
$\frac{24}{50}=48%$2450=48%
When doing percentage calculations you will come across quantities in different units of measurements.
For example, we might want to find out what percentage $65$65 cm is of $3$3 m.
In these situations it is important to mathematically convert one of the units into the other.
Practice questions
Question 3
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.