# Count On

## Explorer

#### Calculator Patterns 2

When we write a fraction, such as 1/891, we are also writing a formula - in this case "1 divided by 891" which we can evaluate on a calculator as:

There seems to be a pattern in these digits. If we do the division by hand, we can get a few more digits than we can on a calculator:

Have we made a mistake - there seems to be only one 8 instead of two? No, we haven't. Carrying on with our long division by hand, we get:

**Can you ... ** find a few more decimal places and spot the pattern?

891 is 81 times 11. What is 1/81 then?

We don't even have *any* 8's this time!

** Can you ... ** find a few more decimal places and spot the pattern?

Also, 9/81 = 1/9 = 0.11111111111111 ...

** Can you ... ** fill in this table and spot any patterns in it?

8/81 = ?

17/81=?

26/81=?

What about this series of fractions?

1/81 = ?

19/81 = ?

28/81 = ?

37/81 = ?