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| Symbol for percent is % |
For example, suppose there are 100 students enrolled in a lectureclass. If only 63 attend the lecture, then 63 per 100 studentsshowed up. This means 63% of the students attended the lecture.
If we take a closer look at this, we can see that the fractionof the students that attended the lecture is 63/100, and thisfraction 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 areclosely related. In fact, they can each be used to represent thesame information.
In this unit we will convert percents to decimals and fractionsas well as convert fractions and decimals to percents. (NOTE: If youfeel you need a review of fractions before moving on you can workthrough the Review of Fractionstutorial in this series.)
Converting between Percents and Decimals
In the box below are the rules for converting between decimalsand percents. Feel free to write them down so you can look atthem if you are having problems.
Convert from Percent to DecimalDivide the percent by 100. This is equivalent to moving the decimal point two places to the left. Convert from Decimal to PercentMultiply 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 multiplyby 100. This is the same as moving the decimal point twoplaces 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%
Convertingbetween 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 writethese down so you can look at them later.
Convert from Percent to Fraction
Convert from Fraction to Percent
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Convert from Percentto 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 thedenominator is 100. Once this is done, we can simplify the fraction.For example, if we wish to convert 10% to a fraction, we (1) dividethe 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 Fractionto Percent
Now let's look at converting a fraction to a percent.As shown above, this is a two step process.
- Convert the fraction to a decimal.
- Convert the decimal to a percent.
If we want to convert 1/4 to a decimal, we divide 1 by 4 andget the decimal, then convert that decimal to a percent.
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| 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%
