Recurring decimals to fractions

Sample Recurring decimals to fractions questions

A few of the 42 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 14 marksGrade 4
   Convert $0.\dot{7}\dot{6}$ (0.767676...) to a fraction.
   Show the worked solution

   Let x = 0.767676... M1

   100x = 76.767676... M2

   100x − x = 76.767676... − 0.767676... = 76 M3

What are the common mistakes in Recurring decimals to fractions?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Gives a rounded decimal answer where an exact form (fraction, surd, or multiple of pi) was required

  Gave a rounded decimal (0.101) instead of the exact proved fraction

• Uses the wrong number of 9s in the denominator when converting a recurring decimal to a fraction

  Used only one 9 in the denominator (9) instead of 90 - with one non-repeating digit and one repeating digit, the correct method needs $100x - 10x = 90x$, not $10x - x = 9x$

Quick answers about Recurring decimals to fractions

How many Recurring decimals to fractions practice questions are there?

There are 42 self-marking GCSE and IGCSE Maths questions on Recurring decimals to fractions, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Each one is marked instantly and has a full worked solution.

Do I need an account to practise Recurring decimals to fractions?

No. You can start practising Recurring decimals to fractions straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.