Question

How can we write `3.11....` (repeated) as fraction?

Answer 1

`3.1` repeated`=28/9=3 1/9`

Explanation:

`3.1` repeated can be written as `3.11111111111............`

and when a single digit, say `k` (where `k` is a natural number from `1` and `9`) is repeated after decimal point, the result is `k/9` plus the number before decimal.

Hence, `3.1` repeated is `3 1/9` i.e. `28/9`
There is another way too.

Let `x=3.1111111.......` and then

`10x=31.111111..........`

Subtracting former from latter we get

`9x=31-3=28`

i.e. `x=28/9=3 1/9`