# Converting percents

The examples below show how to change between percents and decimals and fractions. Being able to do these conversions not only helps when students need to answer questions, they also help when comparing fractions and ratios that are expressed in these different ways.

There are also many situations in language where, for example, stating "approximately one-third" would be more appropriate than stating "approximately 33.3%". The examples below show the following types of conversions

You will find help here with converting fractions to decimals and help here with decimals to fractions.

## Percent to fraction

Percent can be thought of as a ratio with a base of 100. Ratios can be written as fractions. So to convert a percent to a fraction we make the numerator on the top the percent value and make the denominator at the bottom 100. This fraction can often be simplified as shown in the example below.

Write 35% as a fraction.

The numerator is the percent value and the denominator is 100

35
100
We can simplify by dividing top and bottom by the greatest common factor.
 35 ÷ 5 = 7 100 ÷ 5 20

Sometimes the conversion can be a little trickier as the two examples below show.

### Percents with decimal parts

What if the percent includes a decimal part?

Example: 12.5%

We have to get rid of the decimal. In this case multiplying the top and bottom by 2 will do the job.

 12.5 x 2 = 25 100 x 2 200
Now we just need to simplify.
 25 ÷ 25 = 1 200 ÷ 25 8

### Percents over 100

What if the percent is greater than 100?

Example: 110%

We have an improper fraction. The denominator is still 100. In this case we can simplify the fraction.

 110 ÷ 10 = 11 100 ÷ 10 10

## Fraction to percent

The easiest way to convert from a fraction to a percent is to divide the numerator by the denominator and then multiply by 100.

Write the fraction below as a percent.

5
8

Divide top by bottom and multiply by 100

(5 ÷ 8) x 100 = 62.5
Remember to add the % sign.
 5 = 62.5% 8

Very often, when expressing a fraction as a percent, you will need to round to a certain number of decimal places. There is more on rounding decimals here.

## Decimal to percent

To convert a decimal to a percent, multiply by 100

 Write 0.45 as a decimal. Multiply by 100 and add the percent symbol. (0.45) x 100 = 45%

Watch out for when there are more or less than two decimal places. When converting decimals that mostly have two decimal places (e.g. 0.32), it can be easy to think of just removing the decimal place. As the examples below show, the decimal place moves two places to the right with a zero added if required.

 Write 0.2 as a percent. Multiply by 100 and add the percent symbol. (0.2) x 100 = 20% Write 0.6785 as a percent. The percent might still have a decimal part. (0.6785) x 100 = 67.85%

## Percent to decimal

A percent is a ratio with a base of 100. So, to change a percent to a decimal, remove the percent symbol and divide by 100

 What is 55% as a decimal. Divide by 100 (move the decimal point left 2 places). 55 ÷ 100 = 0.55

Do not be caught out by the temptation to always place the decimal point to the left of the digits in the decimal. Although this works for many situations (between 10% and 99%) it does not work for percents less than 10 and more than 100. The two examples below show this.

 What is 4% as a decimal. Divide by 100 (move the decimal point left 2 places). 4 ÷ 100 = 0.04 Write 225% as a decimal. Expect a whole number part when converting percents over 100%. 225 ÷ 100 = 2.25

## Percent/ Decimal/ Fraction conversions to memorize

Memorizing or at least being able quickly recall the equivalent percents, decimals, and fractions listed below will be of great assistance to students as they tackle problems that require changing between the different types. Quick recall of these will also help in everyday-type-situations such as comparing price discounts. e.g. what's the best deal, one-third off, or 25% off?

 Percent Decimal Fraction 10% 0.1 1 10 25% 0.25 1 4 50% 0.5 1 2 75% 0.75 3 4 100% 1 1 Percent Decimal Fraction