GPS Coordinates - Eish! Eina!

Every now and then some Tom-Tom or Garmin fan sends me an email complaining that the GPS coordinates printed on a map are "all wrong".
... and every now and then we get on to Google to find the location of someone's B & B, so we can locate it correctly on our map ... and when we enter the co-ords in Google Earth we find  - for example - that the Tranquillity Backpackers, Nature's Valley, free canoe in every room, is located in an empty part of the Klein-Karoo near De Rust. Or that other larny guest house, street address Ladismith, who locate themselves in northern Zambia.

Both of which problems would be entertaining if they were not so damn frustrating. The problem with GPS readers, useful as they are, is that they introduced a large number of enthusiastic people to a set of basic mathematical principles that lots of those guys didn't understand.
So here goes, Kaartman's Guide to Long/Lat, or Please Either work in Decimals or in Base 60, but not in Both. Please.

Early navigators got it into their heads to divide the surface of the Earth by a set of imaginary lines running around the Earth, through the North and South Poles. These are called lines of longitude, and there are 360 of them, called Degrees. Why not 100 or 400 or 1000? Well, mainly because 360 is divisible exactly by 2, 3 and 5. Early navigators didn't have digital calculators, they had to do sums in their heads [seems incredible, doesn't it?] Because the guys who invented this crazy system lived and worked in Greenwich, near London, England they numbered the line that ran through their lab Number 0 [zero].

They also divided the earth from north to south into degrees, with line Number 0 running around the Equator, and 90 more lines that are parallel with that one, going North, and 90 lines going South. They called these lines of latitude.

They soon found that at the Equator, for example, longitude degrees were more that 100 km apart, as were the latitudes, so they needed some smaller units. In their infinite wisdom they divided longitude and latitude degrees into 60 divisions called "minutes", and each minute into 60 divisions called "seconds" - rather like time has hours, minutes, seconds. 60 is also divisible exactly by 2, 3 and 5, you see.

However, Modern Man and Modern Woman [that's us] like using decimals, which most of us don't understand so we have dinky little electronic gizmos to do it for us. We measure where we are with our tame Garmin and it says something like "32.075643786°S, 22.118796567°E". We have no idea what that means, but it's comforting to know that we are somewhere on Earth. Then we hop into our 4x4 LUV and set the Tom-Tom to find our destination. It gets to a right turn and it says "34°15'00"S, 22°30'00"E" - but even though John Cleese's disembodied voice says we must turn right we are confused, because the map says "34.2500°S, 22.5000°E". Goodness me, the map must be wrong because Cleese never lies.
What we are not seeing is that the map has the coords in decimals, but the Tom-Tom has them in deg/min/sec, or Base 60, not Base 10, so the numbers just ain't gonna be the same, are they?

So please, before you send me another email, check that we're using the same mathematical system.

Oh yes, another thing - GPS readings that have more than 4 decimal places are generally nonsense. It's amusing to read that your B&B is at 32.075643786°S, but nine decimal places means you are measuring to the millimetre - not really necessary to find you!

Hope this helps!

-- Die Kaartman