jmc

Let $x=0.\overline{54}$. Then $100x=54.\overline{54}$, and $100x-x=54.\overline{54}-54⟹99x=54$. Therefore, $0.\overline{54}=\frac{54}{99}$. This simplifies to $\boxed{\frac{6}{11}}$, when both the numerator and the denominator are divided by $9$.