Answer:
6/11
Step-by-step explanation:
To convert a repeating decimal to a fraction, multiply the number by 10^n, where n is the number of repeated digits. Then subtract the original number, and put that result over the denominator 10^n -1.
Here, that means you will have ...
[tex]x=0.\overline{54}\\\\100x=54.\overline{54}\qquad\text{n=2: $10^2=100$}\\\\100x-x=54.\overline{54}-0.\overline{54}\\\\99x=54\\\\x=\dfrac{54}{99}\\\\\boxed{x=\dfrac{6}{11}}[/tex]
