All:
In thinking about this I have remembered that some of the old square tables used to include both numbers for framing square use and often one number was tongue length (16). It is either stamped on or implied that 16 is 16.../16 and in plan view the side cut, perversely drawn on the top, is 45 degrees or 16/16. Remember this is the angle between hips not the hip and a common. My calculations for a 1/12 common rafter pitch octagonal roof find the square settings for the hip side cut as 13'0-5/16 (rafter length) and 12'11-5/16 tangent
(not trig term but carpenters talk long lost) length) yields 16'1-1/4 / 16. A discussion of this use of tangent can be found in the conference proceedimgs from Roanoke on the TFG homepage.

With this in mind lets think about jack numbers:
SIde cut of jack is the ratio:length of common to length of eave. For a 12 foot run, 1/12 pitch the rafter length is 12'0-1/2 and the eave is 4'11-5/8. If you solve for the similar triangle with a 16' leg the result is 6'7-1/4.

We could talk multiple decimal points and finer measurements but this, I believe, is what you are seeing.

Best regards,

curtis