Question 23207
Your question was to express 0.01 as a fraction.  This would simply be 1/100.


However, what I think you meant was 0.01 with a line over the "01", which means a repeating decimal.  It means 0.0101010101 . . . continuing the pattern FOREVER!


If this is the problem, then you are correct to say
Let x=0.01010101 . . .

100x = 1.01010101 . . .


Next, subtract 100x - x:
100x = 1.01010101 . . .
`-x = -0.01010101 . . .
_____________________
99x = 1.00000000


Divide both sides by 99, and you get 
{{{99x = 1}}}
{{{x=1/99}}}


R^2 at SCC