Answer
$1.234\overline{567}=\frac{45679}{37000}$
Work Step by Step
$1.234 \overline{567}= 1.234 + 0.000567+ 0.000000567+.... = 1.234 +\sum_{n=1}^\infty 567(10)^{-6}(0.001)^{n-1}$
The series above is geometric, hence of the form $\sum_{k=0}^\infty a r^k=\frac{a}{1-r}$, where $a= 567(10)^{-6}$.
$1.234 \overline{567}= 1.234+\frac{567(10)^{-6}}{1-0.001}=1+\frac{8679}{37000} = \frac{45679}{37000}$
