Game center state vs app state

Let's say that the player beats the first five levels of whatever game, and they get an achievement for that. Each first level counts toward 20% of that achievement -- so all five is 100%.

They decide to delete the game at one point, and decide to reinstall the game later.

This means that they have to go through the first five levels again since the app state is lost. Should the game:

a) Reset game center achievements to be in sync with app state (that "level beaten" achievement is set to 0% again).

-OR-

b) Update achievement ONLY if the player makes MORE progress in relation to what is in game center.

Option b) seems better here. If the gamer finishes with three levels beaten (achieved 60%), deletes game, then reinstalls, option b) means that the achievement stays at 60%. It only updates if they beat more than three levels when the play the reinstalled game.

Another quick question: percentages are stored as doubles in game center. I guess they are fairly accurate. This means that if I take an old achievement percentage, add some increment on top of that, then set the new total value to the (old achievement % + increment %) value, then I don't have to worry about any sort of error? Assuming I do this many, many times? I'm guessing not, but I am OCD.