 # Convert Recurring Decimals to Fractions

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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. 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

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