BMW Repair: BMW 318.i S, limited slip differential, inch alloy wheels

Question
THANKS FOR THAT.AS I AM BASED IN IRELAND IT WILL PROBABLY BE A MINI ADVENTURE TRYING TO LOCATE PARTS AND GET THE JOB DONE! I HAVE TWO MORE QUESTIONS IF THAT IS OK. I BOUGHT THE CAR WITH 17 INCH ALLOY WHEELS.THE SPARE HAS RADIUS 17 IMPRINTED ON THE TYRE BUT THE FOUR OTHER TYRES HAVE RADIUS 16.IS THIS A PROBLEM.ALSO HAVE YOU HEARD ANYTHING ABOUT THE TRACTION CONTROL FEATURE BEING CONTINUALLY ON?EVEN WHEN I PRESS THE BUTTON AND THE LIGHT COMES ON THE DASHBOARD THE TRACTION CONTROL STAYS ON.ONCE AGAIN THANK YOU FOR YOUR TIME AND PATIENCE.
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-----Question-----
I JUST BOUGHT MY FIRST BMW. SHE IS A 318.iS AND SHE IS FANTASTIC.ONE LITTLE NIGGLY THING. I LET HER RUN FAIRLY LOW ON FUEL JUST TO SEE MILES PER GALLON BUT WHEN I REFUELLED HER THE GUAGE STUCK ON EMPTY. PLEASE HELP.IS THERE ANY QUICK FIX. THANK YOU
-----Answer-----
Paul, not many quick fixes on BMW's. The fuel level sending units are the culprits. I believe your car has two, right and left sides. Running it low on gas didn't cause this, it just help to reveal an existing problem. Have both senders replaced because if you only replace one then Murphy's laws says you will replace the other shortly.
The senders are accessed under the rear seat cushion. They have a plastic retaining ring that requires a special tool to remove.
-Evan

Answer
Paul, the traction control light being on continuously means that there is a fault or malfuntion in that system. Faults need to be read out to determine what the vehicle is seeing. Technically speaking "Yes" the tire and wheels all have to be the same size. If the wheel and tire combinations have the same overall diameter then the traction control won't know the difference. If you have a limited slip differential in the rear and use unequal tires then the differential can be damaged, but I don't believe that you have one so I wouldn't worry.
-Evan