Recurring Decimals to Fractions worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

1. 5 marks
   (a)

   Write the recurring decimal \(0.\dot{ 5 }\) as a fraction.

   Give your answer in its simplest form.

   (b)

   Write the recurring decimal \(0.\dot{ 6 }\dot{ 5 }\) as a fraction.

   Give your answer in its simplest form.

2. 3 marks

   Write the recurring decimal \(0.2\dot{ 8 }\) as a fraction.

   Give your answer in its simplest form.

3. 3 marks

   Write the recurring decimal \(0.\dot{ 1 }4\dot{ 8 }\) as a fraction in its simplest form.

4. 6 marks
   (a)

   Write \(\frac{ 7 }{9}\) as a recurring decimal.

   (b)

   Write \(\frac{ 7 }{11}\) as a recurring decimal.

   (c)

   Prove that \(0.\dot{9} = 1\)

5. 4 marks
   (a)

   Write \(2.\dot{ 8 }\dot{ 2 }\) as a mixed number.

   Give your answer in its simplest form.

   (b)

   Write \(2.\dot{ 8 }\dot{ 2 }\) as an improper fraction.

6. 5 marks
   (a)

   Write the recurring decimal \(0.\dot{ 5 }\) as a fraction in its simplest form.

   (b)

   Write the recurring decimal \(0.\dot{ 6 }\dot{ 0 }\) as a fraction in its simplest form.

7. 3 marks

   Write the recurring decimal \(0.4\dot{ 7 }\) as a fraction in its simplest form.

8. 3 marks

   Write the recurring decimal \(0.\dot{ 8 }9\dot{ 1 }\) as a fraction in its simplest form.

9. 6 marks
   (a)

   Write \(\frac{ 4 }{9}\) as a recurring decimal.

   (b)

   Write \(\frac{ 3 }{11}\) as a recurring decimal.

   (c)

   Prove that \(0.\dot{9} = 1\)

10. 4 marks
    (a)

    Write \(2.\dot{ 3 }\dot{ 4 }\) as a mixed number.

    Give your answer in its simplest form.

    (b)

    Write \(2.\dot{ 3 }\dot{ 4 }\) as an improper fraction.

← All GCSE maths worksheets