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

$${\frac{{\mathtt{0.99}}}{{\mathtt{100}}}} = {\frac{{\mathtt{99}}}{{\mathtt{10\,000}}}} = {\mathtt{0.009\: \!9}}$$