Incidentally, these magic numbers of 111,111 are easy to remember by knowing some history: the French originally defined the meter so that 10^7 meters would be the distance along the Paris meridian from the equator to the north pole. Thus, 10^7 / 90 = 111,111.1 meters equals one degree of latitude to within the capabilities of French surveyors two centuries ago.
So its not just a coincidence, it was defined that way!