Question

Convert into fraction:

$0.4\overline{23}$.

Answer 1

Let $x=$ $0.4\overline{23}$

or, $10x=4.\overline{23}$......(1)

or, $10x=4.23\overline{23}$

or, $1000x=423.\overline{23}$.....(2)

Now subtracting (1) from (2) we get,

$990x=419$

or, $x=\frac{410}{990}$.