Question

How do you find the repeating decimal 0.427 with 427 repeated as a fraction?

Answer 1

`0.427427427427........=427/999`

Explanation:

Let `x=0.427427427427........` ...............(A)

therefore `1000x=427.427427427427........` ...............(B)

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

`999x=427` and `x=427/999`

As only prime factors of `999` are `3` and `37`, which do not divide `427`, we cannot reduce this and

`0.427427427427........=427/999`