## A Real Example of a Percentage Change

Imagine that a company sells 100 calculators in a week. The next week the company sells 120 calculators. The percentage change from 100 to 120 is 20%.## How to Find a Percentage Change

100 to 120 is a percentage change of 20%. How do we know it is 20%?- The
*change*from 100 to 120 is the difference between the numbers.120 − 100 = 20The**change**is 20. - The
*percentage change*expresses the change (20) as a percentage of the original number (100).20 =The**20%**of 100**percentage change**is 20%.

how to find a percentage change

## Other Questions with a Percentage Change

In the example above, we found the percentage change from an old number to a new number. You need to use percentage changes in other ways:- You need to be able to find the new number if you are told the old number and the percentage change.
For example, if a £10 an hour wage increased by 20%, you would have to work out that the new wage would be £12 an hour.

- You need to be able to find the old number if you are told the new number and the percentage change.
For example, if there are 33 students in a class after a 10% increase, you would have to work out that there were originally 30 students in the class.

## Why Is a Percentage Change Useful?

You will see percentage changes used all the time if you read the news. The economy grew by 3%. Crime has fallen by 1%. Profits are up 2%. Why do we use percentage changes? We often need to describe the change from one number to another number. We could just write the difference between the numbers. Imagine 2 companies selling cars:**Company A**and

**Company B**.

**Company A**sold 10 cars last week and 20 cars this week.**Company B**sold 100 cars last week and 110 cars this week.

**Company A**doubled the number of cars it sold from 10 to 20. This is a very impressive 100% increase (because the 10 extra cars are 100% of the 10 cars sold last week).**Company A**did a lot better than**Company B**because it improved much more in a week. Only the percentage change shows this.

## Percentage Increase, Percentage Decrease

In this lesson, we found that the percentage change from 100 to 120 is 20%. This is a**percentage increase**because the number has increased: 120 is larger than 100. The percentage change is positive. If a number decreases (for example, from 100 to 80) then there would be a

**percentage decrease**. The percentage change would be negative.

## You might also like...

percentagesexpressing a number as a percentage of another numberfinding a percentage changeconverting a percentage to a fraction

#### Help Us Improve Mathematics Monster

- Do you disagree with something on this page?
- Did you spot a typo?

__this form__.

#### Find Us Quicker!

- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add
**#mm**to your search term.

#### Share This Page

If you like Mathematics Monster (or this page in particular), please link to it or share it with others.

If you do, __please tell us__. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.

## Worksheet

This test is printable and sendable