If you are cutting a piece of wood with a handsaw and your boss gives you a centimeter ruler and asks for a third, 33 centimeters is about as precise as you can get, and there's certainly a mark for that. That infinitely repeating 3 in the decimal form of 1/3rd in Base-10 can certainly be irritating, but in the real world we don't have infinitely precise tools and can often settle for "good enough".

(Yeah, problems factoring 3s is a deficiency in Base-10 but Base-10 more often than not is "good enough" in practice.)