解：?$(1)$?設?$0.\dot {2} \dot {7}$?為?$x$?，
由?$0.\dot {2} \dot {7} =0.2727...$?，可知?$100x=27.2727...$?，
所以?$100x-x=27$?
解得?$x=\frac {27}{99}=\frac {3}{11}.$?
所以?$0.\dot {2} \dot {7} =\frac {3}{11} .$?
?$(2)$?設?$0.\dot {2}1 \dot {6} =x$?，
由?$0.\dot {2}1 \dot {6} =0.216216...$?，可知?$1000x=216.216216... $?，
所以?$1000x-x=216$?
解得?$x=\frac {216}{999}=\frac {8}{37} .$?
所以?$0.\dot {2}1 \dot {6} =\frac {8}{37} .$?
