The simplest form of $0.\overline{54}$  is:

We are given the recurring decimal $0.\overline{54}$  and it is to be written in simplest form.
To express $0.\overline{54}$  in the form of $\frac{p}{q}$ , assume this number as, say x, and it can be written in the expanded form as follows,
$x=0\cdot \mathrm{54545454.......}$ ……….. (i)
To shift the decimal point by two places to the right, we multiply the equation (i) by 100 on each side as follows, 
$100x=54\cdot \mathrm{545454.....}$ …………. (ii)
Now, we subtract equation (i) from (ii) and simplify as follows,
$\begin{array}{c}100x-x=\mathrm{54.545454.....}-\mathrm{0.545454.....} \\ 99x=54 \\ x=\frac{54}{99}\\ x=\frac{6}{11}\end{array}$ 
So, from the above result, we can conclude that,
$0.\overline{54}=\frac{6}{11}$ .
So, it is the required simplest form.
Hence, the correct option is (2).