Question

How do you convert 4.078 (78 being repeated) to a fraction?

Answer 1

`2019/445`

Explanation:

Let `4.0787878787878...........=x`

Multiplying this by `10`, we get

`10x=40.787878787878...........` -----------------(A)

Multiplying (A) by `100`, we get

`1000x=4078.787878787878...........` -----------------(B)

Now subtracting (A) from (B), we get

`990x=4038` i.e.

`x=4038/990=2019/445`