AI generatedNumberGCSE Higher

Fractions to recurring decimals

Use division and watch the remainders. A repeated remainder makes the same digits repeat.

  • Use division and watch the remainders. A repeated remainder makes the same digits repeat.
  • When a fully simplified denominator has a prime factor other than 2 or 5, its decimal recurs.
  • Use dots to mark the repeating block, or show a correct decimal prefix followed by an ellipsis.

Example 1

Convert the fraction to a recurring decimal. Use dots to show the repeating block.

Bring down a zero. The next digit is 1.Bring down a zero. The next digit is 2.

Example 2

Convert the fraction to a recurring decimal. Use dots to show the repeating block.

Bring down a zero. The next digit is 1.Bring down a zero. The next digit is 3.

Remember
Use the worked steps to check your method, not just the final answer.

Your turn

Question 1

Convert the fraction to a recurring decimal. Use dots to show the repeating block.

Check answer
Bring down a zero. The next digit is 1.Bring down a zero. The next digit is 4.

The starting remainder returns, so the displayed block repeats forever.

Question 2

Convert the fraction to a recurring decimal. Use dots to show the repeating block.

Check answer
Bring down a zero. The next digit is 1.Bring down a zero. The next digit is 5.

The starting remainder returns, so the displayed block repeats forever.

Question 3

Convert the fraction to a recurring decimal. Use dots to show the repeating block.

Check answer
Bring down a zero. The next digit is 1.Bring down a zero. The next digit is 6.

The starting remainder returns, so the displayed block repeats forever.

Question 4

Convert the fraction to a recurring decimal. Use dots to show the repeating block.

Check answer
Bring down a zero. The next digit is 1.Bring down a zero. The next digit is 7.

The starting remainder returns, so the displayed block repeats forever.

Question 5

Convert the fraction to a recurring decimal. Use dots to show the repeating block.

Check answer
Bring down a zero. The next digit is 1.Bring down a zero. The next digit is 8.

The starting remainder returns, so the displayed block repeats forever.

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