When running a 2000 Chevy Monte Carlo fuel gauge falls to empty even when full why?

GM has had some issues with the fuel sending units in the fuel tank doing exactly what yours is doing and the cause is due to sulpher build up. I have a 2004 Corvette and some of those drivers experienced the identical problem. There is an additive called TECHRON you can get at Pep Boys or AUtozone or Walmnart usually best price. Add the proper amount of Techron to your fuel tank and run a few bottles through it and see if it helps. The Techron is said to remove the sulpher build up. Then go to Google and do a web search for TOP TIER Gasolines. There are certain fuels out there that already have the Techron in it. There are some fuels listed that maybe you could change to and never face this issue again. If you can't get the fuel isted in yoru area, then if the Techron works, then pu tin in every 5 tankfuls. This is what I tell anyoen who is experiencing this issue to do first. The Techron never hurts and sometimes it saves lots of money compared to the alternative of dropping the fuel tank and cleaning the fuel sending unit. Good luck