There is no reason why fractional reserve banking could not be done with bitcoins. After all, it existed when the U.S. was on the Gold Standard.
It can't be done with bitcoin, because you cannot produce more bitcoins like you can dollar bills...And when the banks have to fufill the loan, they will have to send actual bitcoins to fund the loan....
Person A deposits 100 BTC. The bank A loans 90 BTC to person B.
Person B deposits 90 BTC. The bank B loans 81 BTC to person C.
Person C deposits 81 BTC. The bank C loans 72 BTC to person D.
Person D deposits 72 BTC. ...
Total apparent number of bitcoins in the system: 1000
That's classic fractional reserve banking and it works with dollars, bitcoins, gold, or seashells.
Incorrect.
If that were true we wouldn't have such an extreme increase in the money supply, national debt, and inflation. The way the Fed and banks in the US works is this:
Person A deposits 100. The bank then creates on book 900 to use for loans and credit=1000 Bam, money created out of thin air.
The banks do this for every deposit that is made, and new money is created "on book" for the additional 9/10s of the fractional reserve rule. This is what results in the highly compounding increase in the money supply. In reality, the actual physical money supply that exists couldn't even pay off the interest on the outstanding national debt.