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The factor for metres to feet is 3.289 A simple way for me is to multiply by 3 and add 10 percent Eg 15m is 3x15=45, 45=4.5 =49.5. 15x3.289=49.33 so it's within an inch. The smaller the number of metres the smaller the difference and since it only really matters at shallower depths this method works very well.
A nautical mile is one minute (not 1 second) of arc on the latitude scale which is 1/60th of a degree.
The original metre was derived from 1/10,000,000th of the distance from the equator to the north pole.
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