If you edit your text in a terminal and use a light weight browser: Asus' E203MA has been working well for me. The CPU is slow. There's not much RAM. I wouldn't run Gnome on it. XFCE, Mate, i3 have all been good.

It's underpowered, it's cheap, but wow does the battery last forever (10 hours).

Beware: Ubuntu's palm rejection is very poor out of the box. No palm rejection issues on Arch or Mint.