You don't need to put an entry for your first fill with a new vehicle. I wouldn't because there is no way of knowing how much gas, if any, has been added during those miles, and the Fuelly log is to record my fuel economy with the vehicle. I would first fill the tank up to start with a topped off one, and reset the trip odometer. The second fill will be the first one I put into Fuelly with miles entered from the trip display.
I use trip for recording miles. As long as you reset it at each fill, I think it is the easier method. If you prefer the odometer, or the car simply doesn't have a trip one, you need to account for those previous owner miles. With a brand new car, I would just leave the few hundred miles tallied up moving the car on and off transports and such in the first Fuelly entry. They will skew the data for it because they weren't on that gas. They will soon be averaged out over the thousands of miles you hopefully have the car. With a used car, make a note of the odometer miles during your first fill, and subtract it from the number for each Fuelly fill.
With partial fills on Fuelly just put in the gas added and miles driven to that point. Just like a total fill. It will not generate a data point for it. So you won't see any off numbers it might generate. Once a full fill is entered, the partial fill(s) will be calculated into the car's averages (mpg, fill cost, tank distance, etc.)
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