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

Feb 24, 2017

$0.427427427427 \ldots \ldots . . = \frac{427}{999}$

#### Explanation:

Let $x = 0.427427427427 \ldots \ldots . .$ ...............(A)

therefore $1000 x = 427.427427427427 \ldots \ldots . .$ ...............(B)

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

$999 x = 427$ and $x = \frac{427}{999}$

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

$0.427427427427 \ldots \ldots . . = \frac{427}{999}$