What you're actually asking here is better to rephrase as
"Whether is 1=0.9999999... ?"
Googling on this would be possible to find myriad forum threads concerning this question. The answer does exist though.
Both "1" and "0,9999999..." denote the same real number. Indeed, real numbers are something that exist independently of our attempts (like numeral systems, which as we see can be quite ambiguous ) to represent them.
The rigorous proof of this fact comes from axiomatic definition of real numbers. Either by Dedekind cuts or Cauchy sequences.
Also note, between any different real numbers there always is another one (continuous property). There is no such number between "1" and "0,99999999...". Then they represent the same number.
- here is a good link concerning this problem.