Question

Express $0.1\overline{23}$ as a rational number in simplest form.

Answer 1

Let x=$0.1\overline{23}$ (bar on 23)

10 x= $1.\overline{23}$ -----(i)

1000x=$123.\overline{23}$ -----(ii)
Subtract eq(ii) from eq.(i)

1000x-10x= $123.\overline{23}$ - $1.\overline{23}$

9990x = 122

x= $\frac{122}{990}$