Question

express 0.9999999.... in the form of p/q

Answer 1

Let x = 0.9999…
There is only one repeating digit so multiply by 10 we get 
10x = 9.9999…
x = 0.9999…
subtract x now we get 
9x = 9
Divide by 9 we get 
x = 9/9 = 1
It justify the answer because approximated value of  0.999999......... is 1

Answer 2

Let 0.9 be x
multiply 10 to both sides
0.9*10=10*x
9.9=10x
9+0.9=10x
9+x=10x
9=9x
9/9=x
1=x