there's no such thing as 1/3?

correct

Actually, 0.33333,,, rounds to 0.333. It's 3, not 4. The number of places to the right of the decimal determines the degree of precision. When expressed as a fraction, 1/3 in exactly that. Exactly. But as a decimal, it can't be expressed exactly.

It's not like pi, which is both an irrational number AND a transcendental number. Pi can't be expressed exactly as a fraction m/n, where m and n are both integers, and can't be produced by any finite series of algebraic operations on integers.

But that's not true of 1/3. The fraction 1/3 is EXACTLY 1/3. If you believe "there's no such thing", try hitting yourself on the head with 1/3 of a twenty-pound iron bar.

okay i am going to try and explain this so bear with me.

The way two numbers are different from each other is that there is a "difference" that if you were to take one number and subtract the other there would be a difference meaning that there is a "number" between the original two numbers. but in the case of .999 repeating to infinity and 1. There is no possible number beteween .9 repeating and one so mathematicians have decided that it is okay to say that .9 repeating is the same as 1. In that case if 1/3 is equal to .3 repeating and you add .3 repeating +.3 repeating + .3 repeating you get .9 repeating which is the same as one. That is my understanding of it. your logic is very good, but in some cases the super duper smart math dudes just make the rules so that everything falls into place and this is one of those cases. Hope that helps!

The fundamental flaw in your question is assuming that decimals fractions are more accurate than real fractions.

(1/3 + 1/3 + 1/3) = (3/3) = (1/1) = 1

Decimal notation is only a means of representing a value, and for fractions it is only an approximate representation. I would suggest looking into the difference between a "number" and a "value". I would also suggest checking out non-decimal number systems like binary, octal, and hex.

And your point is what?