10:10 almost exactly

Watches in advertisements are usually shown with the minute and hour hands in roughly the 10:10 position. For the watch model below, I wanted to know exactly what time it was when the hands are in opposing positions.

I can't get an exact time because the answer appears to be an irrational number. Based on the results of the spreadsheet summarized below, the time is approximately 10:09:13.8461472.


time decimal 0.423076923 days

--------------------Hour--------Minute-----Second
--------------------hand---------hand-------hand

Units Indicated--10.15384615---9.23076912 13.8461472
Angle-----------304.6153846°--55.38461472°
Angle from vert.-55.38461544°-55.38461472°
Difference--------0.00000072°