It's rounding off to the nearest full pixel, that's why it doesn't like .075.
(assuming 6.875 is inches).
It seems to be this way in CS% as well but I found a work around. Now this will at first sound like something you tried but which did not work but it does work.
Select the Crop tool and then set thw width in the control panel to 6.875 and crop the image from left to right. Now look at the image size dialog and you will see you have a 6.875 document.
I do not know why this works and any other wy does not. But it works.
It does not appear to be doing so. It seems to be a bug.
Setting the crop tool to a specific width does seem to correct this at least for that specific file.
At 300 dpi (which I'm guessing you're using):
2062 pixels is 6.873 inches
2063 pixels is 6.877 inches
Since you can't have a fraction of a pixel, you can't get exactly 6.875 inches at precisely 300dpi.
You could change the resolution slightly, or go up to the next whole number of pixels: 2063 = 6.877 inches.
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OK. I just ran a quick check at 300 ppi.
At 2063 pixels, you get 6.877.
At 2062 pixels, you get 6.873.
At 2064 pixels, you get 6.880.
So assuming this is correct (haven't done the math), you'd end up with 2062,5 pixels.
But at other resolutions the numbers could match up better.
Edit: cross-post (obviously).
Wade, in your Crop Tool settings, are you specifying a different ppi value? You could end up getting resampling that way, and so it may be that you can get an exact 6.875 inches.
Question for the original poster: If it's important to be able to achieve 6.875 exactly (to the 1/1000th inch in accuracy), why not use 1000 ppi?
Noel, yeah, I could get 6.875 at 400ppi, 1000ppi, etc. Still the publisher wants it to be 300ppi, not higher, so I guess I'll have to ask 'em if they're sticker for this 6.875 or willing to accept 6.877 instead.