Fractions terminate if their denominators have only 2s and 5s as prime factors.

The prime factors of the denominator of 1/4 are only 2 and 5

1/3 has a larger numerator than 1/4

0.9 recurring is exactly equal to 1 because there is no number between them.

Because 0.9 recurring is equal to 1

Because the number of nines is infinite, so it must exceed 1

Because 0.9 recurring is an irrational number

Because the difference is too small to be measured

Multiplying by a power of 10 aligns the recurring digits so they cancel out during subtraction.

To eliminate the recurring part by aligning the decimal places

To make the number a whole integer

To shift the decimal point to the right of the entire number

To increase the value of the decimal to make it easier to divide

AQA GCSE Maths

Recurring decimals & fractions

AQA GCSE Maths revision on Recurring decimals & fractions. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.

Sample questions (3 of 16)

Question 1

Which of these best explains why 1/3 is a recurring decimal while 1/4 is a terminating decimal?
- A) 1/3 has a larger numerator than 1/4
- B) The prime factors of the denominator of 1/4 are only 2 and 5
- C) 1/3 is a prime fraction
- D) 1/4 is a larger value than 1/3
Show answer

Answer: The prime factors of the denominator of 1/4 are only 2 and 5

A fraction in its simplest form terminates if and only if the prime factorisation of its denominator contains no prime numbers other than 2 or 5. Since the denominator of 1/4 is 2 squared, it terminates, whereas the denominator of 1/3 is 3, which causes it to recur.
Question 2

A student claims that 0.9 recurring is slightly less than 1. Why is this claim mathematically incorrect?
- A) Because 0.9 recurring is equal to 1
- B) Because the number of nines is infinite, so it must exceed 1
- C) Because 0.9 recurring is an irrational number
- D) Because the difference is too small to be measured
Show answer

Answer: Because 0.9 recurring is equal to 1

If you let x = 0.999..., then 10x = 9.999.... Subtracting the two equations gives 9x = 9, meaning x = 1. Therefore, 0.9 recurring is simply another way of representing the integer 1.
Question 3

When converting a recurring decimal to a fraction using algebra, what is the primary goal of multiplying the decimal by a power of 10?
- A) To make the number a whole integer
- B) To eliminate the recurring part by aligning the decimal places
- C) To shift the decimal point to the right of the entire number
- D) To increase the value of the decimal to make it easier to divide
Show answer

Answer: To eliminate the recurring part by aligning the decimal places

By multiplying the decimal by 10, 100, or 1000, you create two equations where the infinite recurring tails are identical. Subtracting these equations removes the infinite decimal portion, leaving a simple integer equation.

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Sample questions (3 of 16)

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