How long will shredded carrots keep? How long will carrots that I've shredded in the food processor stay good in the fridge?  Also what's the best way to store them?
According to the website StillTasty, fresh, raw whole or cut up carrots will last 2 to 3 weeks in the fridge.

I would think that it would be a shorter time (1 week) for shredded carrots.  I'd store them in a container with a tight sealing lid, or in a plastic bag with the air squeezed out.