解:$(2)①0.\dot {7}=0.777···$,$0.\dot {7}×10=7.777···$,
因为$0.\dot {7}×10-0.\dot {7}=7$,所以$0.\dot {7}=\frac {7}{9} .$
$②0.\dot {23}=0.232323···$,$0.\dot {23}×100=23.232323···$,
因为$0.\dot {23}×100-0.\dot {23}=23$,所以$0.\dot {23}=\frac {23}{99} .$