Yikes. No sooner had I posted my previous message than I realized that my example had a serious flaw:
Even if you only have to save a small number of digits to the left of the MSB of the value that you’re currently adding to the total, you have to save ALL the digits to the right. So, at the very first step, -1/3 = -0.33333… Obviously, you have to save all those digits to the right in order to add something to them later.
Ugh. Bad example. Humble apologies.