\(1.27272727...=1.(27)\\\\x=1.(27)\ \ \ \ |multiply\ both\ sides\ by\ 100\\100x=127.(27)\\\\100x-x=127.(27)-1.(27)\\99x=126\ \ \ \ |divide\ both\ sides\ by\ 99\\\\x=\dfrac{126}{99}\\\\x=\dfrac{126:9}{99:9}\\\\x=\dfrac{14}{11}\\\\Answer:\boxed{1.(27)=\dfrac{14}{11}=1\dfrac{3}{11} }\)
