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I've inherited some 20 year old waypoint data that was taken with a Garmin GPS. I don't recognize the lat/lon coordinates as DMS, decimal minutes, or decimal degrees. Here's one record as an example: Lat 4531.38153 Long 12347.2328. I know the very general location of this record to be Lat 45 degrees, Lon -123 degrees.

Can somebody tell me the format of these coordinates so I can convert to decimal degrees?

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They look like Degrees Decimal Minutes (DDM) with the degree and minutes symbols dropped.

Try reading Lat 4531.38153 Long 12347.2328 as Lat 45° 31.38153' Long 123° 47.2328'

You may find this PGC Coordinate Converter useful.

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I suppose it might be NMEA. It has quite strange coordinates representation: lat is DDMM.MMMMM and lon is DDDMM.MMMMM.

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