First: thank for asking an easy question, Kevin. Often our Forum questions are imponderable! However, I hope you meant the first option was ddd.ddddd as Martin assumed, not as you wrote i.e. “ddd°mm.mmm”,
Second: thanks for a succinct, accurate answer, Martin. Right on!
Third: Increasingly, I find degrees and decimal degrees is the preferred format in use – it is the standard in aviation. It reduces the confusion over what units are in use (in radio communications especially and avoids dividing/multiplying by 60. The bad part is that it is harder to use with a nautical chart, because it doesn’t give the minutes which are clearly given on charts, so it is harder to quickly locate the correct point from a given coordinate.
Most sailors, mariners and I prefer ddd mm.mmm – degrees are separated from minutes but we don’t bother with seconds – we just use a decimal of a minute. This is a practical hybrid format that works well with marine charts.
The last option uses seconds instead of decimal minutes and I think this is too confusing for people although it is time-honoured and traditional. I find I make more mistakes over units when using this format. However, the Govt of Canada sticks doggedly to this older format for issuing notices etc so you need to know what it is and how to convert.
The great part about these machines (GPS, plotters etc) is that they don’t really care and can instantly convert from one to another format, so I often re-set my GPS to another of these formats to capture a new waypoint given to me in a format that I don’t currently use – then I switch the machine back and everything is converted into my preferred format, whatever that might be.
Sorry – my explanation was far from succinct!