[lisper]

You can do that, but then the "last digit" doesn't behave the way you intuitively expect it to. For example, 0.0...1 is exactly equal to 0 for the same reason that 0.999... is exactly equal to 1. So you can't add them up to get a non-zero number.

The reason that adding numbers with a finite number of zeros before the first non-zero digit works to give you any number is that that carries go off to the left. But if there are an infinite number of zeros before the first non-zero digit then there will remain an infinite number of zeros after every addition. The carries can only "overcome" a finite number of zeros.