2005 honda civic lx fuel sensor

I've noticed awhile back when I'm on a hill and I am about 3 notches from
an empty tank, it will go down to "E" and the fuel light will come on. Now, I
don't even have to be on a hill and be a few notches from the light coming
on and it will drop down to "E" until I start driving and go back up a little.
What do you think the problem is? Its confusing me. Its not a big
significance like as if I fill up almost all the way and it goes down to E, but I'd
still like to know what the problem is. Thanks!