Introduction

In this lesson, you will learn how to change a decimal into a percent and a percent into a decimal. This is important to know in the next lesson.

This video illustrates the lesson material below. Watching the video is optional.

• Converting Between Decimals and Percentages (07:00 mins) | Transcript

Out of One Hundred

A percentage means an amount out of one hundred. Although the word percent means out of one hundred, percentages can work even if the whole you are using is not 100.

Example 1
If this unit square is divided into ten equal parts, and then three of them are marked, it would be represented as 0.3, or three out of ten, because this is in the tenths column.

To convert a decimal to a percent, multiply by 100 because a percent is out of one hundred. The decimal 0.3 can also be written as the percentage 30%.

Figure 1

Example 2
If that same unit square is divided into one hundred, and three out of the hundred are marked, that would be represented as 0.03 because it is three out of one hundred. The three is in the hundredths place.

To convert to a percent, multiply by 100, or move the decimal two places to the right. The percentage would be 3%.

Figure 2

Example 3
Similarly, if nine out of one hundred were marked, it would be 0.09.

To convert to a percent, multiply by 100, or move the decimal two places to the right. The percentage would be 9%.

Figure 3

Example 4
If 36 out of 100 squares were marked, it would be 0.36.

To convert to a percent, multiply by 100, or move the decimal two places to the right. The percentage would be 36%.

Figure 4

Converting Decimals into Percentages and Percentages into Decimals

Consider some conversions between decimals and percentages.

When converting from percentages to decimals or decimals to percentages, you always move the decimal two places.

Things to Remember

• When converting a decimal to a percent, move the decimal point two places to the right.
• When converting a percentage to a decimal, move the decimal point two places to the left.

Practice Problems

1. Write 12% as a decimal. (
   Solution

   x

   Solution: 0.12
   Details:
   All percentages are out of 100.
   
   \(\displaystyle \stackrel{\text{Percent}}{12\%}\)
   
   Remove the percent sign and replace it with a decimal point. Include a zero as a place holder.
    
   
   Move the decimal two places to the left. Include a zero as a place holder.
    
   \(12\% = 0.12\)
   )
2. Write 125% as a decimal. (
   Solution

   x

   Solution: 1.25
   Details:
   All percentages are out of 100.
   
   \(\displaystyle \stackrel{\text{Percent}}{125\%}\)
   
   Remove the percent sign and replace it with a decimal point. Include a zero as a place holder.
    
   
   Move the decimal two places to the left.
    
   \(125\% = 1.25\)
   )
3. Convert the decimal 0.35 to a percent. (
   Video Solution

   x

   Solution: 35%
   Details:
   

   
   
   | Transcript)
4. Convert the decimal 0.0015 to a percent. (
   Solution

   x

   Solution:
   0.15%
   )
5. Convert the decimal 2.45 to a percent. (
   Solution

   x

   Solution:
   245%
   )
6. Convert 12.3% into a decimal. (
   Video Solution

   x

   Solution: 0.123
   Details:
   

   
   
   | Transcript)
7. Convert 0.92% into a decimal. (
   Solution

   x

   Solution:
   0.0092
   )