You don't have to take your ratchet apart to find out if it is fine tooth or not.
Do you have a vice? Simplest way is to hold the drive end steady (vice or on a socket in your hand) and turn the ratchet one full revolution. Count how many times it clicks in that one full revolution. I'm guessing 36 times. If less, it's pretty coarse, if several more, it's pretty fine.
Or you could just look at your ratchet, tell us here what it says (brand - part number) on it and someone here can tell you.
Do you have a vice? Simplest way is to hold the drive end steady (vice or on a socket in your hand) and turn the ratchet one full revolution. Count how many times it clicks in that one full revolution. I'm guessing 36 times. If less, it's pretty coarse, if several more, it's pretty fine.
Or you could just look at your ratchet, tell us here what it says (brand - part number) on it and someone here can tell you.