we could trade 80 billion shares a day... it doesnt matter until people start HOLDing the shares and locking them away.
10,000,000,000 Auth means thats is total amount of shares they can offer out. 6,xxx,xxx,xxx Outstanding is total shares actually in someones "hands" able to freely trade... of those 6 billion outstanding and ABLE to trade there is a FLOAT. Some shares are held by insiders and other entities possibly and they have locked up their shares and are not trading them... so that lowers the amount of shares that are trading even more... thats THE FLOAT those remaining shares that you see moving around from day to day.