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Calculator Patterns 2

those were the days 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:

1 / 891 = 0.0011223344..

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:

1 / 891 = 0.001122334455667789..

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:

1 / 891 = 0.001122334455667789001122334455..

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


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

1 / 81 = 0.01234567901..

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 = ?

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