not really sure, but saw this:
http://www.proz.com/kudoz/italian_to_french/textiles_clothin...

- I was going to say I don't think we say seven-eighths length and suggest three-quarter length, but it seems we do - is this a fur coat, by any chance?

Indigo fox seven-eighths length coat
http://www.theminkbarn.com/talidis-furs-fox-1.php

These days are no different as we see men pushing the fashion envelope with three-quarter-length coats that hit low on the thigh or at the knee, and the seven-eighths-length coats that swing low down on the leg.
http://findarticles.com/p/articles/mi_m1077/is_4_59/ai_11286...

In the collection Maud Frizon did for us she used Persian lamb as a wrap jacket, as a motorcycle jacket and as a seven-eighths coat that can be worn over any length skirt.''

http://www.nytimes.com/1987/08/29/style/consumer-saturday-th...

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Note added at 2 days11 hrs (2010-03-17 09:41:20 GMT) Post-grading
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By the way, I think it means a couple of inches or so above the knee in length, like the Mink Barn pic. shows and the NYT link says - ''The seven-eighths length, just above the knee, is by far the biggest-selling fashion we've had in five years,'' Mr. Schulman said. - i.e. 7/8ths of the full length, which is to the knee.