Gas Gauge/Sending Unit problem

Having problems getting gauge to read correctly. I fill the tank and needle goes just over full. As I drive I notice the gauge starts to go toward E. At around 50 miles orso gauge starts moving faster eventually ending below E. I’ll once again fill the tank and it will take around 9 gallons. That’s after around 120 miles.

this afternoon I wanted to check the gauge by ground in the hot wire. The tank was about half full. When the hot wire was grounded the gauge would go from below E to 1/2 tank. I’m thinking the sending unit is the problem. By the way the tank was recently replaced and appears the sender is new.