Black on fins, yes that is fin rot. Fins just tearing, that's not fin rot.
In which case, he's in a .5 right? You should do a 100% change every day and use 1 tsp per gallon of Aquarium salt, please dissolve it before you put it in because when salt dissolves it releases and makes heat which can burn your fish soooo that's no good! So for a .5 you use .5 teaspoons of salt, dissolve, put it in slowly over about half an hour. Then the next day, scoop him out, change all the water, use conditioner and put it .5 teaspoon of salt again. Then you should acclimate him to the new water and release him gently when he's acclimated after 30-45 minutes.
When introducing salts it's better to take your time with acclimation since they can be a bit tough on the system so take more time if you can, up to an hour with acclimating salts. Also, don't use the AQ salt for more than 14 days, it can cause liver/kidney malfunction which leads to a dead >< that's not good either!
And if you can, use Stress Coat at double dose when you condition your water with it, this helps heal fins after the rot is gone.
If you need me to elaborate anything, feel free to ask and I will ^_^