two comments:
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you are confusing wrapped and unwrapped. “xu, yu, zu” are unwrapped coordinates, i.e. include the distance traveled through periodic boundaries. “x, y, z” are wrapped coordinates, i.e. bounded by the principal cell (with minimal exceptions as explained in the dump command documentation).
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how accurate you can convert one into the other after the fact depends on the precision with which to store or enter coordinates and box dimensions into your conversion code. keep in mind that if an atom has traveled through the box multiple times, the error due to the lacking precision of the box is multiplied.