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Herman Dekker, Yes. Really you don't have to go any further than one minute of arc. Decimalized, that's 0.016666... degrees. That makes sense since it's one-sixth divided by ten. The rest are just integer multiples. The key cases that you should be able to do in your head are the "twentieths" of a degree, which are all the multiples of three minutes of arc. Multiples of six minutes are easy; they decimalize as tenths: 18' is 0.3°, 24' is 0.4°, 54' is 0.9°. Then if you add three minutes to any of these values, you end up adding 0.05° to the decimalization: 21' is 0.35°, 27' is 0.45°, 57' is 0.95°. Of course this is just for those cases where you're trying to do it in your head. Otherwise it's trivial on a calculator --of course!

The common theory, unprovable but certainly plausible and widely accepted, is that the mixed decimal/sexagesimal system of Ancient Mesopotamia was convenient because 60 has numerous factors which greatly simplify division. And who knows, maybe it originated in an even more ancient civilization long ago submerged by post-glacial sea level rise in the Persian Gulf. We use sexagesimal measure for time-keeping and angle measure to this day, but at least in angle measure it's finally being replaced by decimal degrees. Geographic and astronomical coordinates are now commonly given as decimal degrees without further explanation. For example, here's a spot in southern Iraq: 30.962741002841774°N, 46.10309411200602°E. The coordinates were provided by Google Maps with just a wee bit more precision than required for "most" practical purposes ;).

Unlike our modern use of sexagesimal, limited now to time and angular measure, in Ancient Mesopotamia, this was the standard numbering system in almost all facets of life. Property contracts spelled out the dimensions of farm fields in sexagesimal. And here's an example of something more esoteric: 1°24'51"10"'. That's 1 (not degrees, just "units") and 24 minutes, 51 seconds, and 10 thirds. Decimalize that value. Does it look familiar? It's a bit of mathematical trivia, calculated to remarkably high precision, that dates back some 3600 years, which also happens to be a nice sexagesimal number :).

Frank Reed