Convert Recurring Decimals to Fractions

The following diagram shows how to convert a recurring decimal to a fraction. Scroll down the page for more examples and solutions of how to convert a recurring decimal to a fraction.

• Convert between Decimals & Fractions Worksheets

  Printable
  Convert Decimals to Fractions
  Convert Decimals to Mixed Numbers
  Convert Repeating Decimals to Fractions
  

  Convert Fractions to Decimals (denominator 10, 100, or 1000)
  Convert Fractions to Decimals (use equivalent fractions)
  Convert Fractions to Decimals (use long division)
  Convert Fractions to Repeating Decimals (recurring decimals)
  Convert Mixed Numbers to Decimals
  

  Online
  Decimals to Fractions
  Decimals to Mixed Numbers
  Fractions to Decimals (denominators 10, 100, 1,000)
  Mixed Numbers to Decimals (denominators 10, 100, 1,000)
  Fractions to Decimals using division
  Convert between Decimals, Fractions & Percents
  

How to convert recurring decimals to fractions?

Step 1: Let x = recurring decimal in expanded form.
Step 2: Let the number of recurring digits = n.
Step 3: Multiply recurring decimal by 10ⁿ.
Step 4: Subtract (1) from (3) to eliminate the recurring part.
Step 5: Solve for x, expressing your answer as a fraction in its simplest form.

Examples:
Change the following recurring decimals into fractions
(i) 0.4
(ii) 0.275
(iii) 3.112

• Show Video Lesson

Recurring decimals to fractions part 1 of 2

Changing recurring decimals to fractions.

Examples:

1. Convert the recurring decimal 0.29 to a fraction.
   
   
2. Prove that the recurring decimal 0.39 = 13/33.
   
   
3. Express 0.27 as a fraction in its simplest form.
   
   
4. x is an integer such that 1 ≤ x ≤ 9

Prove that 0.0x = x/99

• Show Video Lesson

Recurring decimals to fractions part 2 of 2

Changing recurring decimals to fractions

Examples:

1. Convert the recurring decimal 0.013 to a fraction.
   
   
2. Convert the recurring decimal 0.36 to a fraction.
   
   
3. Convert the recurring decimal 2.136 to a mixed number. Give your answer in its simplest form.
   

• Show Video Lesson

How to convert recurring decimals to fractions?

Examples:

1. Convert the recurring decimal to fractions.
   (i) 0.444444444444
   (ii) 0.7777777777
   (iii) 0.111111111

2. Convert the recurring decimal to fractions.
   (i) 0.333333333
   (ii) 0.6666666666

3. Convert the recurring decimal to fractions.
   (i) 0.232323232323
   (ii) 0.151515151515

• Show Video Lesson

Convert recurring decimals to fractions

Example:

1. Convert the recurring decimal to fractions.
   (i) 0.413413413413413
   (ii) 0.1444444444444

• Show Video Lesson

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.