330xi low gas mileage

Yes taek it in and have the code read with an engine scan to see whyyou aregetting a lean code. It may be a vacuum leak or a bbad sensor

The Dr. Is back in the house, let me know if I can help here.

If you have a lean code there are many reasons for it including a vacuum leak. If you take choke cleaner around the intake manifold and other placeswhere the throttle body connects it will show your vacuum leak by changing the rpm. However don't spray on the air ducts as this won't show a leak. But the reason you have to go and get the engine scanned is because your O2 sensor cold be bad or you have an injector or injectors running lean causing this. Because alot of peopel don't know what to do or we don't know their expertise on a mechanical thing like a car I always reccomend to take it in to a shop so they can save theirselves money as well as getting the correct diagnosis so you are giving the oil companies the least amount of money possible as well as not doing damage to your vehicle.

The issue might require seeking out someone with the proprietary scan tool to see the live data, fault codes can be great to diagnose, but the whole picture makes for a more complete diagnosis. And yes the engine with a vacuum leak is not running in fuel control and it will distort economy, as you well know.