I am teaching a Year 9 top set and recurring decimals are the next topic on the scheme of work. Before I look at the harder skill of changing a recurring decimal into a fraction I check that they can change a fraction to a decimal so I write on the board
When I ask what ‘over’ means they happily respond ‘divide’ so I demonstrate a ‘bus stop’ division.
They then easily manage to convert three ninths and five ninths so I then get them to work backwards to work out nought point nine recurring as a fraction. I loved their response when they got the answer 1. They just can’t believe that it can get ‘right up’ to 1 even though they have proved it. I remind them that they are happy with
They can see this gives the same result – this helps them to accept it.
We then move on to elevenths and show that
It is worth noting that to avoid repeating a similar calculation many times, exam questions on this tend to be ninths or elevenths.
I then challenge them to find one seventh.Remember that ‘use and interpret notation correctly’ is part of AO1 so if students writethen they may well be penalised. We then have a brief play with the cyclic number 142 857 looking at 2× and 3× it, asking them to explain what is going on and predict 4× and 5× before looking at the beautiful 7 × 142 857.
If time allows, get your students to try converting fractions with longer recurring decimals.One ninety-seventh is a suitable activity for students either:
- as a sponsored divide-athon
- or if you have a Gauss-like student who you need to keep occupied for a while.
The answer is a 96 digit recurring decimal!
Steve Cavill BSc(Hons) PGCE FCIEA has taught maths in both state and independent schools. He spent a few years as an Associate Lecturer for the OU and has written a number of GCSE maths books, workbooks and revision guides as well as being a senior examiner and moderator for GCSE and IGCSE.