First, we are going to give our decimal a name, let's call it x. We notice that x repeats after two digits, so how about we look at 100x.
100x = 54.54545454...
But, the decimal part of this number is what we called x, so let's subtract it.
100x - x = 54.5454545454... - 0.54545454
Working out both sides, we get
99x = 54
So, x = 54/99. However, we are not finished as the question said "in its simplest form". Either notice that 99 and 54 are both divisible by 9, or that they're divisible by 3 twice and we get the final answer.
x = 6/11