How can you convert 0.99999999999999999999... to a fraction?
It is 1
$$let x=0.\bar{9}$$
10x=9.9999999999999...
x=0.999999999999.....
subtract
9x = 9
x=9/9
x=1
Consider that
$${\frac{{\mathtt{0.9}}}{{\mathtt{10}}}} = {\frac{{\mathtt{9}}}{{\mathtt{100}}}} = {\mathtt{0.09}}$$
and that
$${\frac{{\mathtt{0.99}}}{{\mathtt{100}}}} = {\frac{{\mathtt{99}}}{{\mathtt{10\,000}}}} = {\mathtt{0.009\: \!9}}$$