You can only get an approximation when using digital computations as explained before: There is not enough memory to store the infinitely long sting of 3's. While 1/3 is an exact, it is mathematically equivalent to .3333333..., because even though 1/3 is more exact, it is a function, and it's result is an irrational number. You can express irrational numbers in visually rational way, but it doesn't negate the fact of their equivalence. 1/3=.333333... no matter how you try and deny it. The computer's software however are designed and coded correctly to understand this and not produce an error in the output, and thus, based on real mathematical rules, will continue to provide extremely accurate results, even correct one's when dealing with such irrational numbers.
When I perform (1/3)+(1/3), I get an approximation as well, when traversing the equation the long way on the calculator, but when I add the last (1/3) [so that my button sequence is (1/3[which =.3333333333...]+1/3[which then =.66666666667]+1/3)] I get 1.
When (1/3) = .3333..., and we know that (1/3)*3=1, then we must deduce that .9999... = 1. Basic arithmetic, and backed by a calculator. Learn the rules of simple math's and you should deduce the same instead of being a stubborn calculus nerd who want's to think different.
.99999...=1=(1/3)*3
Still not defeated, next.
To simplify:
(1/3) = .33333333...
(1/3)*3=1
(1/3)+(1/3)+(1/3)=1
(.3333333...)+(.3333333...)+(.3333333...)=1
(.3333333...)+(.3333333...)+(.3333333...)=(.999999...)
(.9999999...)=1
Remember, basic math's.