Buick 2001 Century Owner's Manual page 146

Here are four things that some owners ask about. All
these things are normal and do not indicate that anything
is wrong with the fuel gage:
D
At the gas station, the pump shuts off before the gage
reads full.
D
It takes more (or less) fuel to fill up than the gage
reads. For example, the gage reads half full, but it
took more (or less) than half of the tank's capacity
to fill it.
D
The gage pointer may move while cornering, braking
or speeding up.
D
The gage may not indicate empty when the ignition
is turned off.
2-76
Low Fuel Light
United States
If your fuel is low, a circular light on your instrument
panel cluster will come on and stay on and a chime will
sound periodically until you add fuel.
It will also come on for a few seconds when you first
turn on the ignition as a check to show you it's working.
If it doesn't come on then, have it fixed.
Canada