Stardate composition

 Captain's log, stardate 78207.7.

I was able to reverse engineer the first Picard stardate, 78183.10, to within one milliyear. However, I'm not sure about the fractional part.  I'm just going to assume that it works the same way it did for Kirk and younger Picard, and that the integer, left of the decimal point, represents decimal milliyear, and the fraction, right of the decimal, represents the decimal time of day.

Thus 0.183 x 365 = 67 days, equals March 8

0.10 x 24 = 2.4 hours equals  2:24 - 2:28:24 am.;

For the second stardate, 78186.03,

0.186 x 365 = 68 days, equals March 9

0.03 x 24 x 60 = 43.2 minutes, equals 12:42:12 - 12:57:36 am