Fuel Gauge?

I drive a 1991 Chevy Lumina (about 36,000 miles) and I really don't understand the fuel gauge. When I turn my car off the gauge shows me how much gas I have. So if I have half of a tank of gas when the car is on, when I turn the car off, the gauge still reads half of a tank. Then when I drive, the needle moves around quite a bit, because it's a floating gas gauge, so it can be hard to tell how much gas I have when I'm driving, so I tend to rely more on what the gas gauge says when the car is parked and turned off, and it has been really accurate until now. It seems that when I get to quarter of a tank of gas or below, every time I turn the car on, the needle goes down to empty, and then when I turn it off after driving, the needle will display an amount that seems more accurate. For example, the gauge will say that I have a quarter of a tank of gas, I'll turn the car on, the needle goes to empty, I'll drive somewhere, and then when I turn the car off again, the needle will show that I have slightly less than quarter of a tank, which is the amount I would expect to have. Well last night, I got stranded because the gauge said I had a little less than a quarter of a tank of gas when it was off when apparently it didn't. Is this a normal occurance with older cars? I really don't understand why the gauge would be more accurate when the car is off and when I have more than a quarter of a tank of gas in it. Could there be something wrong with my car? I've been driving it for over a year now and I didn't have any problems with gauge until maybe two weeks or so ago.