Fuel reading discrepancy

[Stoneybroke]

My car was showing half tank on the gauge but luckily I clicked on the miles check and it said I had 19 miles left. Topped the tank up and level showed the increase. Now down to just over 100 mile range and the tank is showing just under half full. There is a discrepancy between the fuel gauge and the digital display.

Any suggestions?

 

[scm]

The range is a guess based on recent trips, so if you've done a lot of short journeys it'll read lower than after a long motorway cruise. What did the range say after you'd brimmed the tank? How much fuel did the tank take to fill up the empty "half"?