Year 6 maths worksheet: Calculator patterns and recurring decimals

The calculator can prove to be a great tool for those who are fascinated by numbers and these pages give us just one example of this.

It uses simple division sums to produce interesting recurring decimals. For example:

1/9 is 0.111111

2/9 is 0.22222

3/9 is 0.33333

and so on.

It also asks children to use their knowledge of equivalent fractions to see if they can come up with other division questions which also create these patterns. As 1/9 is equivalent to 2/18 then this fraction will also create the same pattern.

A further extension is to ask why this happens and this can be answered by doing the division by written methods where it will soon be noticed that the same remainder keeps recurring, hence the recurring or never ending answer. The numbers can also be continued: 10/9 = 1.111111 etc. Fascinating!!

(A philosophical extra to ask  is why doesn’t 9/9 give 0.999999?)

These pages can be found in our Using and Understanding Maths section for Year 6.

Recurring decimals (1)