To give an answer you need to define what is "13.333... exactly". If you define it as an infinite string to the right, an algorithm that calculates it (using the rules of addition and multiplication) will print it in infinite time. Mentioning the algorithm here is for intuition, in fact if you define operations on infinite strings that way, it will do so. The nerds can refer to the axiom of choice.

(In your post you used the word "approximate". Ask yourself the question -- "approximate what?")