Question

Express 0.99999.... in the form of p/q.
I did and get 9/9, that's equal to 1. But how does it even makes sense? Is 0.9999... equal to 1?
Please explain.

Answer 1

Let x = 0.9999…
10x = 9.9999… Since there is only one repeating digit after the decimal, thus multiply x by 10.
10x = 9 + x
9x = 9
x = 1
The difference between 1 and 0.999999 is 0.000001 which is negligible.
Thus, 0.999 is too much near 1.
Therefore, the 1 as the answer can be justified.