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.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.0 out of 5 based on 151 votes.

Previous Day | This starter is for 6 July | Next Day


Sign in to your Transum subscription account to see the answers

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

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.


Have you read Craig's book yet?

Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...

"How I wish I'd taught Maths" is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL.

The Craig Barton Book

Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

Online Maths Shop

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.

Student Activity


©1997-2020 WWW.TRANSUM.ORG