Convert Recurring Decimals to Fractions

Related Topics:
More Lessons for GCSE Maths
Math Worksheets

Videos, examples, solutions, games, activities, and worksheets that are suitable for GCSE Maths.

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.

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

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

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

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

[?] Subscribe To This Site