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Recurring decimals to fractions practice questions with answers

Higher · Grade 6 · Non-calculator

A second set of recurring decimals to fractions questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

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Question 1 Easy

Convert 0.555... to a fraction in its simplest form.

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Answer: 5/9

  1. One repeating digit 5 sits over 9.
  2. 5/9 cannot be simplified.
  • Method (1): One repeating digit 5 sits over 9.
  • Accuracy (1): 5/9 cannot be simplified.

Question 2 Easy

Convert 0.888... to a fraction in its simplest form.

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Answer: 8/9

  1. One repeating digit 8 sits over 9.
  2. 8/9 cannot be simplified.
  • Method (1): One repeating digit 8 sits over 9.
  • Accuracy (1): 8/9 cannot be simplified.

Question 3 Medium

Convert 0.272727... to a fraction in its simplest form.

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Answer: 3/11

  1. The block 27 repeats over 99.
  2. Cancel 27/99 by dividing top and bottom by 9 to get 3/11.
  • Method (1): The block 27 repeats over 99.
  • Accuracy (1): Cancel 27/99 by dividing top and bottom by 9 to get 3/11.

Question 4 Medium

Convert 0.181818... to a fraction in its simplest form.

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Answer: 2/11

  1. The block 18 repeats over 99.
  2. Cancel 18/99 by dividing top and bottom by 9 to get 2/11.
  • Method (1): The block 18 repeats over 99.
  • Accuracy (1): Cancel 18/99 by dividing top and bottom by 9 to get 2/11.

Question 5 Hard

Find the recurring decimal for the fraction 1/11.

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Answer: 0.09 recurring

  1. Perform division: 1 ÷ 11 = 0.0909...
  2. The two-digit block 09 repeats indefinitely, written as 0.09 recurring.
  • Method (1): Perform division: 1 ÷ 11 = 0.0909...
  • Accuracy (1): The two-digit block 09 repeats indefinitely, written as 0.09 recurring.

Question 6 Hard

Find the recurring decimal for the fraction 4/11.

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Answer: 0.36 recurring

  1. Perform division: 4 ÷ 11 = 0.3636...
  2. The two-digit block 36 repeats indefinitely, written as 0.36 recurring.
  • Method (1): Perform division: 4 ÷ 11 = 0.3636...
  • Accuracy (1): The two-digit block 36 repeats indefinitely, written as 0.36 recurring.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Find the recurring decimal for the fraction 2/3.

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Answer: 0.6 recurring

  1. Divide 2 by 3: 2 ÷ 3 = 0.666...
  2. The remainder is 2 every time, so the digit 6 repeats. State the answer as 0.6 recurring.
  • Method (1): Divide 2 by 3 to get 0.666...
  • Accuracy (1): 0.6 recurring (dot over the 6)

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

Why is 0.777... equal to 7/9?

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The single digit 7 repeats, so the denominator is 9. The single digit 7 repeats, so the denominator is 9.

Check 2

What fraction is 0.222... before you think about tenths?

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2/9, because one repeating digit uses 9. 2/9, because one repeating digit uses 9.

Check 3

What is the denominator for a two-digit repeating block?

  1. 99
  2. 100
  3. 198
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99 99, before you cancel the fraction.

Check 4

How does 0.121212... become 4/33?

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12/99 cancels by 3 to 4/33. 12/99 cancels by 3 to 4/33.

Check 5

Cancel the block in 0.454545... and name the fraction.

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45/99 cancels by 9 to 5/11. 45/99 cancels by 9 to 5/11.

Check 6

Reduce 0.363636... after writing it over 99.

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36/99 cancels by 9 to 4/11. 36/99 cancels by 9 to 4/11.

Check 7

What is 0.454545... as a cancelled fraction?

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45/99 simplifies to 5/11. 45/99 simplifies to 5/11.

Check 8

What is 0.181818... as a cancelled fraction?

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18/99 simplifies to 2/11. 18/99 simplifies to 2/11.

Check 9

Why say equal for 0.777... and 7/9?

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They are two writings of the same number. They are two writings of the same number.

Check 10

Write 1/3 as a recurring decimal.

  1. 2/3 is 0.6 recurring
  2. 1/3 is 0.3 recurring
  3. 2/9 is 0.2 recurring
Show answer

1/3 is 0.3 recurring 1/3 is 0.3 recurring.

Check 11

Turn 2/9 into its recurring decimal.

  1. 2/9 is 0.2 recurring
  2. 2/3 is 0.6 recurring
  3. 1/3 is 0.3 recurring
Show answer

2/9 is 0.2 recurring 2/9 is 0.2 recurring.

Check 12

The fraction 2/3 has which recurring decimal?

  1. 2/9 is 0.2 recurring
  2. 2/3 is 0.6 recurring
  3. 1/3 is 0.3 recurring
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2/3 is 0.6 recurring 2/3 is 0.6 recurring.

Check 13

Which repeating block does 1/11 produce?

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The block 09 repeats: 0.0909... The block 09 repeats: 0.0909...

Check 14

Why not write 0.45 for 0.454545...?

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0.45 terminates while the fraction is exact. 0.45 terminates while the fraction is exact.

Check 15

What should you do after writing the block over 99?

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Cancel the fraction if a common factor exists. Cancel the fraction if a common factor exists.

Keep going with Recurring decimals to fractions

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