If you're wanting to find out the gear ratio, you could either:
- Raise the rear wheels, Drain the gear oil, remove the cover, and count the teeth on both the ring and the pinion. Use a colored grease pencil (at your local h/w store) if you need to make reference marks while turning the wheel to get a full revolution on the ring gear.
Divide the ring tooth total by the pinion tooth total, and you'll have the ratio.
- Or... put a mark / piece of tape on your driveshaft, where you can see it from a rear tire. Place a reference mark on one of the rear tires. Jack up the rear and count how many rotations of the driveshaft it takes to rotate the tire one revolution. This isn't as exact as the first method, but it'll get you close enough, if you know the available ratios for that MY.
Taking a wild-@ss guess, I'll predict you have a 3.73 in the rear, now; the full-size pickups with Z71 of that era had that ratio around then, IIRC.
If you have 4WD, do NOT drive the vehicle with the front driveshaft connected (in any mode) until you verify you have the same gear ratio front and rear. If you have different ones, leave the front shaft disconnected and keep the truck in 2WD until they're both the same ratio again. Your Service Parts Identification label in your glove box should give you the gear ratio that came stock with your Tahoe (it'll have what's called an RPO code, which you can use to cross-reference -- some examples are GT4, GT5, GU6 (and that is NOT a complete list). If you have G80 or G86, that is a limited slip (G86) or locking (G80) differential. The Z71 diff probably has the G80 locker, btw.
As far as altering the ratio, if you have a different one than stock, it can generally be modified with a GM Tech2 diagnostic scanner (or its successor, which the dealer techs use now). Maybe a Snap-On Solus, but I'm not sure on that one. So you could take it to a dealer, if you don't have access to either of those diagnostic platforms; they'll charge you for (at least) one hour of time to change it (even though it will take them less than half of that.)
Do you have a check engine light on in the dash? What codes are present? Barring that, what is happening with the transmission that you suspect there's an issue with it?