You may not need a new battery. I had the issue of the paperwhite re-indexing ALL of my content and getting snagged on a corrupted book toward the end of the process. This looks for all the world like the battery is dying.
Backup your kindle devices folder to a computer.
Delete everything but the book you are reading.
Delete the hidden indexes in the system folder.
Restart the kindle.
Now it should charge to 100% - and last weeks instead of hours.
(search for kindle paperwhite indexing battery re-indexing)