Gas Gage stopped working

First you need to diagnose the problem, which should be about 1 hour of labor. it could be your gauge or your sending unit or wiring etc, etc,

according to a BMW mechanic this is caused by the sending unit which is part of the fuel pump on the passenger side of the tank. Because it is part of the fuel pump they wanted to charge around 450 to replace it. It looks like the part alone can be purchased for around 200