Converting Fractions, Decimals, and Percentages

Are you having trouble figuring out how to convert ⅕ into a percentage? Well, look no further because you’ve come to the right place! We’re going to teach your all about converting fractions, decimals, and percentages, complete with examples and practice math problems so you can follow along! In this blog, we’ll go over the following:

Fractions to Decimals

Fractions to Percentages

Decimals to Fractions

Decimals to Percentages

Percentages to Fractions

Percentages to Decimals

Let’s get started!

Fractions to Decimals

To begin, you want to break down the fraction. The “numerator / denominator” becomes “numerator ÷ denominator” because the slash (/) stands for dividing (÷). For example, 1/2 is 1 ÷ 2. After this, you divide your numerator by your denominator. 1 ÷ 2 is 0.5, so 0.5 is your decimal. 

Example Problem

Let’s convert 1/8 into a decimal.

Steps:

  1. 1/8

  2. 1 ÷ 8 <- “/” is the same thing as “÷”

  3. 0.125

Answer: 0.125

Your turn!

Try converting 2/5 into a decimal.

Ready for the answer? +

Answer: 0.4

Steps:

  1. 2/5
  2. 2 ÷ 5
  3. 0.4

Fractions to Percentages

This takes a bit more work, so pay attention to not miss a step! First, you want to take your fraction and then divide its numerator by its denominator. Ever notice how the slash in fractions represents a division sign? It’s true because if you take a fraction like 1/9, the slash between the 1 and the 9 is a division sign (÷). This means that 1/9 is the same as 1 ÷ 9. After dividing the numerator by the denominator, you get a decimal. Multiply your answer by 100 and add a percent sign.

Example Problem

Let’s convert 6/5 into a percentage.

Steps

  1. 6/5

  2. 6 ÷ 5

  3. 1.2 <- Don’t forget to convert the decimal to a percentage by multiplying by 100! 

  4. 120 <- Make sure to add a percent sign!

  5. 120%

Answer: 120%

Your turn!

Try converting 4/5 into a percentage.

Ready for the answer? +

Answer: 80%

Steps:

  1. 4/5
  2. 4 ÷ 5
  3. 0.8
  4. 80
  5. 80%

Decimals to Fractions

We’ve already learned a lot to this point, but let’s learn how to convert numbers like 0.6 or 0.04 into fractions. To start, you want to divide the decimal at hand by 1. You do this using “/1”. For example, the first step to a decimal like 0.04 would be 0.04/1 because the slash represents a division symbol. This is all it takes, but if you want to get a fraction where a numerator is a whole number, keep reading.

To get a fraction where a numerator is a whole number, keep multiplying the numerator and denominator by 10 until you get a whole number on top. For example, 0.04/1 would be which is 0.4/10. The numerator isn’t a whole number yet, so let’s multiply the numerator and denominator by 10 again. We get which is 4/100. 4 is a whole number, so 4/100 would be the answer we’re looking for!

Example Problems

Let’s convert 0.66 into a fraction.

Steps:

  1. 0.66

  2. 0.66/1

Answer: 0.66/1

Let’s convert 0.23 into a fraction where the numerator is a whole number.

Steps:

  1. 0.23

  2. 0.23/1

  3. 0.23 x 10 ÷ 1 x 10

  4. 2.3/10 <- The numerator isn’t a whole number yet.

  5. 2.3 x 10 ÷ 10 x 10

  6. 23/100

Answer: 23/100

Your turn!

Try converting 0.1 into a fraction.

Ready for the answer? +

Answer: 0.1/1

Steps:

  1. 0.1
  2. 0.1/1

Try converting 1.4 into a fraction where the numerator is a whole number.

Ready for the answer? +

Answer: 14/10

Steps:

  1. 1.4
  2. 1.4/1
  3. 1.410/110
  4. 14/10

Decimals to Percentages 

To turn a percentage into a decimal, multiply your decimal by 100 and make sure to add a percent sign!

Example Problem

Let’s convert 2.91 into a percentage.

Steps:

  1. 2.91 <- Multiply by 100

  2. 291 <- Add a percent sign

  3. 291%

Answer: 291%

Ready for the answer? +

Answer: 3%

  1. 0.03
  2. 3
  3. 3%

Percentages to Fractions

This seems complicated at first, but the process is actually pretty simple! All you do is divide the percentage by 100 and then put “/1” next to your answer (don’t forget to take the percent sign away). If you want the numerator to be a whole number, keep multiplying the numerator and denominator by 10!

Example Problems

Let’s convert 27% into a fraction.

Steps:

  1. 27%

  2. 27/100

  3. 0.27

  4. 0.27/1

Answer: 0.27/1

Let’s convert 30% into a fraction where the numerator is a whole number.

Steps:

  1. 30%

  2. 30/100

  3. 0.3

  4. 0.3/1

  5. 0.3*10/1*10

  6. 3/10

Answer: 3/10

Your turn!

Try converting 45% into a fraction.

Ready for the answer? +

Answer: 0.45/1

Steps:

  1. 45%
  2. 45/100
  3. 0.45
  4. 0.45/1

Try converting 89% into a fraction where the numerator is a whole number.

Ready for the answer? +

Answer: 89/100

Steps:

  1. 89%
  2. 89/100
  3. 0.89
  4. 0.89/1
  5. 0.8910/110
  6. 8.9/10
  7. 8.910/1010
  8. 89/100

Percentages to Decimals

To turn a percentage into a decimal, multiply your decimal by 100 and make sure to add a percent sign!

Example Problem

Let’s convert 24.7% into a decimal.

Steps:

  1. 24.7%

  2. 24.7/100

  3. 0.247

Answer: 0.247

Your Turn!

Try converting 375% into a decimal.

Ready for the answer? +

Answer: 3.75

Steps:

  1. 375%
  2. 375/100
  3. 3.75

Final Thoughts on Converting Fractions, Decimals, and Percents

Hope this was useful! Still need help? Make sure to get in touch with an UPchieve tutor to work with you for free.

Want to learn more about math at your own pace? Check out these resources:

Math & ScienceYukta Pandiri