Question

How can we write `1.5555...........` (`5` repeating endlessly) as fraction?

Answer 1

`1.55555555555...=14/9=1 5/9`

Explanation:

Let `x=1.55555555555...` .........(1)

then `10x=15.55555555555...` .........(2)

Subtracting (1) from (2), we get

`10x-x-=15.55555555555...- 1.55555555555...=14`

i.e. `9x=14`

hence `x=14/9`

i.e. `1.55555555555...=14/9=1 5/9`

Answer 2

`1.bar5=x`.....(1)
`1.bar5 xx 10 =15.bar5=10x`.........(2)
Put equation 1 and 2
`10x-x=15.55555-1.55555`
`9x=14`
`x=14/9`
`x=1 5/9`