The 9.0678 mm value is actually based on a legally non-existant unit that would be an “international inch.” (ie 25.40 mm = 1 int inch)
But the real inch is 12th of a U.S. Survey Foot (the only legally useable foot), which is 0.30480061 meters, thus 25.400051 mm = 1 inch, so .357 = 9.067818 mm.
Thank you!!! I love learning new things. I had seen the term survey foot before, but did not know why. Now I do. I just finished reading the NIST website where I found that it came about from the 1866 law as I have copied and pasted below for those interested:
The U.S. Metric Law of 1866 gave the relationship 1 m = 39.37 in (in is the unit symbol for the inch). From 1893 until 1959, the yard was defined as being exactly equal to (3600/3937) m, and thus the foot was defined as being exactly equal to (1200/3937) m.
In 1959 the definition of the yard was changed to bring the U.S. yard and the yard used in other countries into agreement; see Ref. [7: FR 1959]. Since then the yard has been defined as exactly equal to 0.9144 m, and thus the foot has been defined as exactly equal to 0.3048 m. At the same time it was decided that any data expressed in feet derived from geodetic surveys within the United States would continue to bear the relationship as defined in 1893, namely, 1 ft = (1200/3937) m (ft is the unit symbol for the foot). The name of this foot is “U.S. survey foot,” while the name of the new foot defined in 1959 is “international foot.” The two are related to each other through the expression 1 international foot = 0.999 998 U.S. survey foot exactly.