All of which makes me glad that I rarely need the accuracy beyond 53-bits and when I do, 64-bit ints suffice.

This is why I prefer to keep things as rationals (or bigrats), rather than floats - it's possible to represent them accurately without encountering the inevitable rounding or truncating errors. True, all the irrational numbers will still truncate, but the rationals won't. I only use the decimal representation for display purposes, sometimes.