How can 0.99999... be converted into a proper fraction. Why is that the answer?

Let 0.99999... = p be the proper
fraction.

p = 0.999.....                     
(1).

Multiply both sides of equation at (1) by
10.

10p = 9.999....                   
(2)

(2) - (1):

10p - p =
(9.999...) - (0.999.....)

9p =
9.

p = 9/9 =
1/1.

Therefore p = 1/1. Or p =
1.