You'll definitely have to throw it away at some point.
The art is in making those points well-defined and rare enough to not cause large discrepancies, but frequent enough to avoid ballooning arbitrary-precision numbers across databases and services that might not be able to handle them.
I really like that phrasing! Would you mind if I steal in some form if I decide to review this part of the book?
Not at all, and thanks for writing all of this up!