I am aware that radioactive decay is a form of exponential decay as the common ratio of the decay of a radioactive isotope is 0 < x > 1. So obviously, as with all exponential decay, the number being multiplied by the common ratio will never become zero- just asymptotically approach zero.

However, this is where I am slightly confused- as if you have a finite amount of radioactive substance which has a decay rate between 0 and 1, then surely (given enough time) there will be literally "none" of the substance left; it will all have decayed. Is there some law of physics which prevents the entirety of a substance decaying? As I understand exponential decay in mathematical terms, but not in terms of a finite amount of substance which will continue decaying.