Increasing the bit depth decreases this error, although I'm not sure whether any finite bit depth would be sufficient for error-free conversion. The same problem in one dimension is the use of different base numeral systems to represent values on a number line. Compare base-10 (decimal) vs base-2 (binary). In general, there will be some values that neither system can represent with a literal decimal notation (or even a fraction), irrational numbers, e.g.
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