Answer
(a) 518/99
(b) 124/90=62/45
(c) 2114/990=1057/495
Work Step by Step
(a)
$x=5.\overline{23}=5.232323...$
$100x=523.232323....$
$100x-x=99x=518$
$x=518/99$
(b)
$x=1.3\bar7=1.3777...$
$100x=137.7777...$
$10x=13.777...$
$100x-10x=90x=124$
$x=124/90=62/45$
(c)
$x=2.1\overline{35}=2.1353535...$
$1000x=2135.3535....$
$10x=21.353535...$
$1000x-10x=990x=2114$
$x=2114/990=1057/495$
