Recurring Decimal

Use your calculator to find which whole number divided by another whole number gives the answer:



A Mathematics Lesson Starter Of The Day


Topics: Starter | Arithmetic | Calculator | Fractions

  • N. Cox, Woodbridge Suffolk
  • It would have been good if this was one of those starters where I could get a new question by using the refresh button.

    [Transum: Thanks for your suggestion, there is now a button lower down this page to 'Change Numbers'. Also if you click on the link lower down the page ( for the related student activity you will find more recurring decimals.]
  • The Best Maths Class Ever (7cd/M2), King Alfred's College
  • Many of us found it too hard at the beginning but when we realised what we were doing, we managed to think of lots of answers.
  • Miss Groves, Edinburgh
  • Class 1B3 from Forrester High School Edinburgh were enjoying this very much. We found the answer and then we multiplied up and divided to get other results.
  • J. Miley, Kingsbury School, Birmingham
  • I agree, thank you, though ... it got them thinking!
  • Jill, Knowling
  • A very good starter although once completed you should be able to refresh it.
  • Transum,
  • Thanks for your comments. There is now a button below allowing you to generate a different recurring decimal. There is also a link to a self marking quiz related to this starter below. Did you know that a fraction in lowest terms with a prime denominator other than 2 or 5 always produces a repeating decimal?
  • Mr Kennelly, 3rd Class Mayo
  • My class found it hard to do but then we figured it out. The best one yet I think and the class loved it to :).
  • Ms Polius-Curran, Basildon Upper Academy
  • This starter has to be one of the best differentiated starters I have come across, my Foundation group enjoyed using the calculator to find the two whole numbers whilst my Higher group solved this without the calculator by using the method to convert recurring decimals to fractions.
  • Mr Okungbowa, Northbury Junior School
  • This is very good. I would like more questions like this one because they are really mind boggling and it takes a lot of working out to find correct answers.
  • Sapphire Class, Gloucester
  • We tried this in Y5/6 - the closest we could get is 1000/748 = 1.3368983
    We also noticed that 52/22 = 2.363636.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
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This starter has scored a mean of 3.0 out of 5 based on 130 votes.

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Let the number be represented by x

x = 1.36363636... [1]

100x = 136.363636... [2]

Subtract [1] from [2]

99x = 135

x = 135/99

x = 15/11

The two whole numbers could be 15 and 11

What else could they be?

Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.

A spreadsheet could be used to quickly find a solution to this kind of problem.

Spreadsheet method

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Click the images above to see all the details of these gift ideas and to buy them online.

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Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.

Use a spreadsheet to help investigate which pairs of numbers, when divided, give a recurring decimal answer.

Here is the URL which will take them to a student version of this activity.




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