This is about floating point arithmetic in computers.
Arbitray-precision floating point arithmetic like e.g. GMP offers doesn't suffer these issues.
However, it's possible using MPFR in a way without suffering this issues. One could increase precision every time there would be rounding.
Even if you don't, your required precision blows up very quickly, and your performance drops.
In more general context, you could choose e as the base of your number system and then multiplying by e is a trivial shift. Then, however, multiplying by 2 would make arithmetically no sense. The natural question that arises is whether it's possible to represent all computable numbers non-lossy in one system. The answer is yes.
Besides that, I think you should re-evaluate your decision-making for votes.
Yes. that's kind of my point: Either you have a finite precision cutoff and lose accuracy, or the memory used for your arbitrary precision representation blows up to incredibly large values (transcendentals will do this to you quickly), or a combination of the two.
Its about binary floating point arithmetic in computers, though one could do a similar thing for, e.g., decimal floating point. (Though decimal floating point rounding issues will show up much more rarely in many real-world classes of application.)