The main problem is simply that math is "perfect" and reality isn't. Since math is an abstract description of causality while reality doesn't/can't really "do" infinity.

But if you really wanted to, you could bake a cake in a lab with a predetermined number of atoms and then split that cake into 3 perfect slices. However, once you start counting multiples(like atoms in a cake) you would no longer get 1/3 or 0.3 because you are now dividing a number bigger than 1(the number of atoms) so you would't get a fraction(0.3) You would get a whole number.