in reply to
Computers should have a more accurate representation of real numbers
Interesting idea - and well worth raising.
Perhaps related (but also a little different) is Interval Arithmetic. Just set your precision, do your calculations, and you end up with an upper and lower bound (for the given precision/inputs) - within which the exact value lies.
I've played with a C library, and a perl extension (that I wrote) that wraps that C library .... but only *played*.