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I have 2002 Aurora with the same problem.
Bad gauge Bad float in tank
You need a new fuel pump
I have a 2001 Aurora with the 4.0 V8 and one day, right after filling up my tank, the gas gauge went straight to "empty" and stayed there. I took it to GM and they said my "fuel sending unit" had gone out, along with whatever sensor it has on it. They replaced both in about 4 hours and 450$ and it fixed the problem. Still works fine today over 2 years later.
Faulty signal sender in the tank.
no you need to get it fixed and it will cost alot.
In front of the radiator
That depends entirely on the vehicle and on how accurate the gauge is.
the float could stick
a bad sending unit in the gas tank.
The gauge or sensor needs to be replaced.
The fuel pump may be fine but the sending unit may not be. The sending unit is probably the most common cause of fuel gauge failure.