# Review of Percents

## Objectives

After completing this unit you should be able to:

• Define percent.
• Convert percents to decimals.
• Convert decimals to percents.
• Convert percents to fractions.
• Convert fractions to percents.

## What is Percent?

Given the frequency that percents occur, it is very important that you understand what a percent is and are able to use percents in performing calculations. This unit will help you learn the skills you need in order to work with percents.

In the 1400's, the words "per cento" were used to describe a percent. Today, those words have been abbreviated to the symbol (%). Using this symbol shows that we are comparing a number to one hundred.

 Percent means "per one hundred" Symbol for percent is %

For example, suppose there are 100 students enrolled in a lecture class. If only 63 attend the lecture, then 63 per 100 students showed up. This means 63% of the students attended the lecture.

If we take a closer look at this, we can see that the fraction of the students that attended the lecture is 63/100, and this fraction can be expressed as 0.63.

• 63% is the same as 63/100
• 63% is the same as 0.63

This example shows how decimals, fractions, and percents are closely related. In fact, they can each be used to represent the same information.

In this unit we will convert percents to decimals and fractions as well as convert fractions and decimals to percents. (NOTE: If you feel you need a review of fractions before moving on you can work through the Review of Fractions tutorial in this series.)

## Converting between Percents and Decimals

In the box below are the rules for converting between decimals and percents. Feel free to write them down so you can look at them if you are having problems.

### Convert from Percent to Decimal

Divide the percent by 100. This is equivalent to moving the decimal point two places to the left.

### Convert from Decimal to Percent

Multiply the decimal by 100. This is equivalent to moving the decimal point two places to the right.

### Convert from Percent to Decimal

 To change a percent to a decimal we divide by 100. This is the same as moving the decimal point two places to the left. For example, 15% is equivalent to the decimal 0.15. Notice that dividing by 100 moves the decimal point two places to the left.

### Example

 What decimal is equivalent to 117%? The decimal 1.17 is equivalent to 117%. NOTE: Since 117% is greater than 100%, the decimal will be greater than one. To convert 117% to a decimal, we divide by 100. When we do this we get the decimal 1.17. This is shown on the right.

### Convert from Decimal to Percent

To change a decimal to a percent, we multiply by 100. This is the same as moving the decimal point two places to the right. To change the decimal 0.22 to a percent, we move the decimal point two places to the right and get 22%.

 .22 x 100 = 22%

Look at the example below.

### Example

 Convert 0.55 to a percent. The decimal 0.55 is equivalent to 55%. To convert 0.55 to a decimal, we multiply by 100. When we do this we get 55%. This multiplication is shown on the right. .55 x 100 = 55%

## Converting between Percents and Fractions

It is also useful to be able to convert between percents and fractions. Below are the rules for converting between percents and fractions. Each of these is a two step process. Again, feel free to write these down so you can look at them later.

### Convert from Percent to Fraction

1. Divide the percent by 100 to get a fraction.
2. Simplify the fraction.

### Convert from Fraction to Percent

1. Convert the fraction to a decimal by dividing the numerator by the denominator.
2. Convert the decimal to a percent by multiplying by 100.

### Convert from Percent to Fraction

To convert a percent to a decimal, we divide by 100. This is the same thing we do to convert a percent to a fraction. The number before the (%) sign becomes the numerator, and the denominator is 100. Once this is done, we can simplify the fraction. For example, if we wish to convert 10% to a fraction, we (1) divide the 10 by 100, then (2) simplify the fraction.

Let's look at an example.

### Example

 Convert 0.5% to a fraction. The answer is 1/200. Divide the percent by 100 to get a fraction. Simplify the fraction.

### Convert from Fraction to Percent

Now let's look at converting a fraction to a percent. As shown above, this is a two step process.

1. Convert the fraction to a decimal.
2. Convert the decimal to a percent.

If we want to convert 1/4 to a decimal, we divide 1 by 4 and get the decimal, then convert that decimal to a percent.

 Convert the fraction to a decimal. Convert the decimal to a percent. 0.25 x 100 = 25%

Now let's work an example.

### Example

 Convert the fraction 3/5 to a percent. The fraction 3/5 = 60%. Convert the fraction to a decimal. Convert the decimal to a percent. (Multiply the decimal by 100.) 0.6 x 100 = 60%

You should now be able to convert percents to both fractions and decimals and to convert decimals and fractions to percents. Try the practice for this unit to be sure you understand how to do these.