My take:
Theres a base value for every stat, in your example the piece adds 680 to x (where x is your current base stat for crit chance). Percent bonus (from mods that increase cc by percent) is then derived from that base value and added to it.
I think the game displays total crit as a percent as that's what it is, you have a percentage that may grant you a crit (ie 25% is a 1 in 4, 50% is 1 in 2, etc). The whole number gear adds to the base number that the percent is calculated on.
So say you had a base value of 100 cc; the percent would then be based off that value. Adding your 680 to the 100 now gives you a higher base value, and in turn better chances/higher percent). I'm not sure of the max value cc base can go to, but I image the calculation to figure cc is base value multiplied by any % increases from mods, divided by max value x 100 to give the total cc%
