[cvick]

Technically, you are correct: a single bank cannot do this, but the entire banking system can. With a 10% reserve requirement, a single $100 deposit at one bank becomes $1,000 of credit in the entire banking system.

However, the point that I am trying to make is that you cannot do that with bitcoin because you cannot lend out BTC that you do not have. If you start out with 100 BTC, you can never increase that amount by any kind of fractional reserve lending - there will only ever be 100 BTC.

The idea of "BTC credit" expressed as actual BTC makes no sense -- 1 BTC is 1 BTC it is the thing that is used for trade. If you want to create a new kind of currency that is backed by bitcoin and start a bank that uses that currency for fractional lending, then there is nothing to stop you, but you would have to operate in something other than actual BTC for credit - using actual BTC for that just won't work, as you'll quickly run out of any BTC that you had after only a few transactions/loans.