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These names are three digit numbers starting with 001 and incrementing each time you create a new waypoint.Even if you rename a waypoint the unit will generally assign the next number in the sequence anyway and will not reuse the numbers until it reaches 999.Some folks assign a waypoint to a high number to force a block of numbers to be sequential for a particular use.Storing your present location is the usual way to record a waypoint.Garmin receivers have differing capabilities in the number of waypoints that they can save.The earliest units could save 250 waypoints while later models can store up to 500. In addition some units have additional waypoints that are stored in an internal database.
Finally you should hit "save" to store the waypoint in your database.
The emap, 76 family, and etrex store waypoints in 3 dimensions by including altitude. The 76 family will also store depth data for water if an optional depth sensor is attached.
When you first create a new waypoint the unit will automatically assign it a name.
Satellites close to the horizon will have good satellite geometry when coupled to one high unit but they suffer from atmospheric effects which can make the accuracy worse.
These factors are taken into consideration when the unit reports the estimated position error, EPE on the Satellite status screen.
The accuracy of a particular fix is dependent on a number of factors.