Fuel gauge jumping around

Hello, why was the battery disconnected? Your "distance to empty" indicator is a reading that the computer calculates based on cumulative data. Interrupting the power supply would change this data, and in turn change the results. It's not a scientific display - it's providing information based on data provided. If you lose accurate data, the output becomes less accurate. Drive the vehicle further and in time it will again determine and learn your typical driving habits to get that "average" distance to empty display back closer to reality.