You pick up the bill and suddenly unlock the WALLET! That's convenient, you would sure hate to have to put it in your inventory and drop your awesome stick. Looks like it even has spaces for various cards.

10 TRUE CASH gets added to your wallet. Wait... that's a weird denomination, right? Weren't you thinking of it as a "dollar" before? But you're not sure why you feel that way, because logically you know that's just how money is here. 10 TC sounds perfectly normal and you decide not to pay it any more attention. Into the wallet it goes!