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If a DME fix is in the GPS database, you can navigate to that fix rather than to the navaid. The coodinates for the fix take slant range into account.
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I disagree. I've flown aircraft with both IFR and GPS operating and seen differences of .1 to .2nm when flying directly to a fix. I've also noticed the difference in the ERJ between the DME and the FMS, which is driven by GPS.
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A DME fix is defined by what the DME will read at a given altitude on a given radial, and the DME is slant range, therefore the coordinates of the DME fix will take slant range into consideration.
Is it a DME fix you were flying to, or an intersection of 2 radials that happens to be identifiable by DME? If that is the case, I think you are right that they don't take the slant range into consideration, because you can be at a variety of altitudes, each giving a different slant range, but still probaly has less than .1 error due to the distance to the navaid.
If we are both talking about a DME fix, the ones we find on a DME approach, I think the difference is due to the difference in accuracy of the DME, GPS and altimeter. .1 to .2 is pretty small error as we're only talking about a few hundred feet.