Answer
(a) 7/9
(b) 26/90=13/45
(c) 57/99=19/33
Work Step by Step
(a)
$x=0.\bar7=0.77777...$
$10x=7.77777...$
$10x-x=9x=7.77777...-0.77777...=7$
$x=7/9$
(b)
$x=0.2\bar8=0.288888...$
$100x=28.888....$
$10x=2.888...$
$100x-10x=90x=26$
$x=26/90=13/45$
(c)
$x=\overline{57}=0.575757...$
$100x=57.575757....$
$100x-x=99x=57$
$x=57/99=19/33$
