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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 10^{n}.

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

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.

More Lessons for GCSE Maths

Math Worksheets

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.

Step 1: Let x = recurring decimal in expanded form.

Step 2: Let the number of recurring digits = n.

Step 3: Multiply recurring decimal by 10

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

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

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.

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

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.

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