What are Percentages and How To Calculate Percentages?


By Robert O

How do we define a percentage?

A percentage is a different way of representing fractions or decimals. It represents part of a whole thing that is in question. But instead of leaving the result as a fraction or as a decimal, it is expressed as a percentage. In other words, a percentage means out of 100, where 100 is the whole thing or a complete section. How do you know that a value is in percentage? Usually, the symbol % accompanies the value. An example of value and sign notation is 23%.

Where do we apply percentages?

Think of your scores as a student or a sales tax for a taxpayer. What you get is in percentage. Many applications of percentages exist that we cannot exploit all of them. So, we are leaving that part out for you to find out where you have seen values expressed as a percentage.

How to change a fraction and decimal into percentages and vice versa?

The process is as simple as just multiplying the decimal or fraction in question by 100%.

For example:

    \[\frac{1}{5} \equiv \frac{1}{5} \times 100 \% \equiv 20 \%\]

    \[\frac{1}{2} \equiv \frac{1}{2} \times 100 \% \equiv 50 \%\]

    \[0.25 \equiv 0.25 \times 100 \% \equiv 25 \%\]

    \[0.015 \equiv 0.05 \times 100 \% \equiv 1.5 \%\]

Converting back from percentages to fractions or decimals is also very easy. Just divide the percentage value by 100 to get the decimal representation of the same. If you need fractions, then put the percentage value over 100 and simplify the fraction.

For example:

    \[15 \% \equiv \frac{15}{100} \equiv \frac{3}{20}\]

    \[12 \% \equiv \frac{12}{100} \equiv 0.12\]

We will further explain how to use percentages in representing data using examples.

Example 1

In a class of 50 students, 30 of them got a pass mark on a mathematics test. Calculate the percentage of the students who failed the test.


Be keen on what the question requires. Find the number of students who failed the test by getting the difference between the total number of students in the class and the students who passed the test.

The number of students who failed: 50 – 30 = 20.

Convert this into a percentage of the total test takers:

    \[\frac{\text { Students who failed }}{\text { Total number of students }}=\frac{20}{50} \times 100=40 \%\]

Example 2

John has 5 oranges, 2 apples, and 3 mangoes. What percentage of fruits that John has are mangoes?


    \[\frac{\text { Number of mangoes }}{\text { Total number of fruits }}=\frac{3}{5+2+3} \times 100=\frac{3}{10} \times 100\]

    \[=30 \%\]

Example 3

In a school election for a school head boy, the total number of votes cast is 1000. If the winner got 67% of the total votes, what is the total number of votes the winner got?


In this example, we already have the percentage representing a value. The task is to find this value.

    \[\frac{\text { Percentage winner got }}{\text { Total percentage }} \times \text { Total number of votes cast }\]

    \[=\frac{67}{100} \times 1000=670 \text { votes }\]

Example 4

The current employee’s monthly salary is 5200 dollars after an increase of 200 dollars. What is the employee’s percentage increase in salary?


We have to calculate the original employee’s salary before the increase before calculating the percentage increase.

    \[\frac{\text { Salary increase }}{\text { Original salary }} \times 100=\frac{200}{5200-200} \times 100\]

    \[=\frac{200}{5000} \times 100=10 \%\]

Example 5

Michelle bought a dress at 45 dollars after getting a percentage discount of 10%. What is the market price of the dress that she bought?


If Michelle bought the cloth at 45 dollars after getting a discount of 10%, then it means she purchased it at 90% of the market price. That means:

    \[\frac{90}{100} \times \text { marked price }=\$ 45\]

Therefore, the market price is:

    \[\text { Market price }=\frac{100 \times \$ 45}{90}=\$ 50\]


Regardless of the situation, you can always convert decimals and fractions to percentages and vice versa. If you have a question, understanding what the question is asking for is the key to solving it. You can carry out any operation using percentages as well.

About the Author

This lesson was prepared by Robert O. He holds a Bachelor of Engineering (B.Eng.) degree in Electrical and electronics engineering. He is a career teacher and headed the department of languages and assumed various leadership roles. He writes for Full Potential Learning Academy.