Write the value of
Question:

Write the value of $0 . \overline{423}$ in the form of a simple fraction.

Solution:

Let, x=0.423423423… …(i)

Multiplying this equation by 1000 on both the sides so that repetitive terms cancel out and we get:

1000x=423.423423423… …(ii)

Equation (ii)-(i),

⇒ 1000x-x=423.423423423-0.423423423=423

⇒ 999x=423

$\Rightarrow \mathrm{X}=\frac{423}{999}=\frac{47}{111}$

$0 . \overline{423}=\frac{47}{111}$