Ideas
Convert decimals to percentages
To convert a decimal to a percentage, multiply by 100\%. For example, 0.15 as a percentage or 'per100' is 0.15 \times 100\% = 15\%.
To convert a percentage to a decimal, divide by 100\%. For example, 212\%=\dfrac{212\%}{100\%}=2.12
Examples
Example 1
Convert 0.42 into a percentage.
We can convert any percentage into a decimal by dividing the percentage value by 100, which is equivalent to decreasing the place value of each digit by two places, and removing the \% symbol.
Convert fractions to percentages
Given a percentage is out of 100, a percentage can be written as a fraction with a denominator of 100. To convert a percentage to a fraction, first write the percentage as the numerator, place 100 in the denominator and then simplify if possible.
For example, 28\% = \dfrac{28}{100} which simplifies to \dfrac{7}{25}.
To convert from a fraction to a percentage, convert to a fraction with 100 as the denominator. For example, to write \dfrac{4}{5} as a percentage, multiply the top and bottom by 20.
| \displaystyle \dfrac{4}{5} | \displaystyle = | \displaystyle \dfrac{80}{100} |
| \displaystyle = | \displaystyle 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 to convert to a percentage. For example, to write \dfrac{1}{3} as a percentage, first convert to a decimal by dividing the numerator by the denominator to get \dfrac{1}{3}=0.333....
Multiplying by 100 give 33.333... so \dfrac{1}{3}=33.3...\%which can be expressed exactly as 33 \dfrac{1}{3}\%or approximately by 33.3\%.
Examples
Example 2
Convert \dfrac{5}{10} into a percentage.
We can convert any fraction into a percentage by finding its equivalent fraction that has a denominator of 100. After this, we can write the value in the numerator followed by the \% symbol to represent the percentage.
Find 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.
Examples
Example 3
Find 71\% of 526\text{ L}.
To calculate the percentage of a quantity, convert the percentage into a fraction or a decimal and then multiply by the quantity.
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\text{ L} of water in it but it can hold a maximum of 50\text{ 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 \dfrac{24}{50}. This question could also be asked as follows, what percentage is 24 of 50?
To convert it into a percentage we can use equivalent fractions to make the denominators 100:
| \displaystyle \dfrac{24}{50} | \displaystyle = | \displaystyle \dfrac{48}{100} |
| \displaystyle = | \displaystyle 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 cm is of 3 m.
In these situations it is important to mathematically convert one of the units into the other.
Examples
Example 4
There are 2 boys and 7 girls in a class.
Find the total number of students in the class.
What percentage of the class is boys?
What percentage of the class is girls?
To find a quantity as a percentage, first write it as a fraction with the quantity as the numerator and the whole as the denominator, then multiply the fraction by 100\%.