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 write
then 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!
Many thanks,
Steve Cavill
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.