Let us say that I would like to store latitudes and longitudes like this:
lat 35 degree
long 80 degree
Which system of units does the unit 'degree' belong to? It is not really a SI unit nor a Imperial unit ...
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Degrees are part of a modified Sexagesimal (base 60) number system. Even though there are 360 degrees in a circle, 360 is 6 x 60. The origin of degrees as angular units is unclear (see wiki/Degree_(angle)#History.)
See Coordinate Conversion: Decimal Degree to Deg-Min-Sec of lat/long Coordinates for subdivisions of a degree.
In terms of fundamental physical units, mass, length and time, angles are actually unitless because they are derived from ratios of lengths:
For a sector: arc angle = arc length / radius
For a right triangle: angle
= arcsine (opposite / hypotenuse)
= arctan (opposite / adjacent)
= arccosine (adjacent / hypotenuse)
We still give a name to those natural unitless angles: radians.
2 π radians = 360 °
For data storage, you can use any units, so long as you have proper conversions to/from those used in the interfaces. Radians are most readily suitable for trigonometric functions, but then, if you use direction cosines, you can avoid some (costly) trigonometric functions.