Well, there is no way to represent one third in decimal form in a 10-digit number system. Even if 0.333 could trail 3's forever, it wouldn't actually ever become 1/3: it would merely be infinitely approaching 1/3.
In other words, 1/3 doesn't actually equal 0.333... and 2/3 doesn't actually equal 0.666... Those numbers just represent values increasingly close to those exact ratios.