Can fractions actually be converted to decimals? I was working on a spreadsheet in Excel (I'm a plebe, I know), and I came across a fraction that actually equated to 33.3% of a total number. While looking at it, and looking at the number that went with it, I realized that fractions of 1/3 continue on ad infinitum. 
My question is this:
Can fractions accurately be converted to decimals without rounding or assuming that .000 ad infinitum = 0 and still have the numbers reach the intended and proven result?
I don't wish for this to be specifically for Excel. I'm asking for more of a theoretical question about the continuation of fractions to an infinite number of places. 
From what I know of fractions, 1/3 would equate to .333... ad infinitum. By my reasoning, the difference between 1 and "3/3" would be infinitesimally smaller the further you go. With that logic TECHNICALLY 9.99... != 10.0 or is there something I'm missing? I understand that in practice the numbers match, but given infinite places, when graphed the numbers would never intersect, but would get infinitesimally smaller. 
Example: 3.33.... + 6.66.... = 9.99.... != 10.00....
Given an infinite number of decimal places, then 
Note: I have no idea how to use the MathJax equations. If anyone wants to edit that in, I'd be appreciative.
 A: Technically, 
$$9.\overbrace{9\ldots9}^n < 10$$
for any finite number $n$ of $9$s after the decimal point.
Also, technically,
$$9.\overbrace{9\ldots9}^n < 9.\overline9$$
for any finite number $n$ of $9$s after the decimal point;
the number on the right has an infinite number of digits and the
number on the left doesn't.
Certainly if you put any finite number of $9$s on the right of the
decimal point, no matter how large a finite number of $9$s you put there
you will always have a number less than $10$.
But you also won't have $9.\overline9$.
So what is $9.\overline9$ after all?
To quote from this answer to the question "Is $0.999999999\ldots = 1$?",

Symbols don't mean anything in particular until you've defined what you mean by them.

If we want to define $9.\overline9$ so that it has a meaning and
actually represents a real number rather than a different mathematical object altogether, the definition that generally makes sense is that it
is a limit of an infinite series, and when we look more carefully to see
what that limit is, we find that it is $10$. Not just very, very close
to $10$, but actually equal to $10$.
A: If the number of digits is finite (which is always the case in an Excel sheet), the answer is no.
For example, the fraction $1/3$ can not be expressend with a decimal number with finitely many digits.
In general, if the fraction is in its lowest terms and the denominator has a prime factor different from $2$ or $5$, the corresponding decimal number will have infinitely many digits.
A: The decimal representation of rational numbers come in two forms: either they terminate or a finite pattern emerges. In your case this pattern in $1/3$ is just $3$ repeating over and over again.
Whether a fraction terminates is interesting and depends on the number system you use. If you have a reduced fraction of the form
$$\frac{1}{a} $$
This fraction will terminate whenever the prime divisors of $a$ are only $2,5$, the same one's as $10$'s, the base of our decimal system. 
One of the advantages of working say base 60 (as the babylonians did), is you have a lot more terminating fractions, since $60=2^2*3*5$ has more prime divisors. 
