We do not have a fractional reserve banking system. Banks create deposits out of thin air.

Answering the question "Does the U.S. have a fractional reserve banking system?"

From Quora::

No. The U.S., as well as pretty much every other country, uses what is better described as a credit creation system.

In a true fractional reserve system, banks collect and then lend out 'hard' currency, in the way we have all learned from the old story. It is easiest to think of hard currency as coins – the bank has 100 coins; it can lend out 90, and keeps 10 on hand in reserve. The next bank collects those 90 coins; they can lend out 81, and keep 9 in reserve, etc., etc., until you end up with the same 100 coins in existence, plus 900 in bank accounts. Bank lending is limited by the amount of hard currency in existence. By extension, cash withdrawals are limited as well.

The way banks actually operate is by creating credit on ledgers. Loans are “funded” 100% with credit; if you take out a $1000 loan with $200 in interest, your bank simply marks up your account by $1000, and holds your promissory note, nominally worth $1200, as their asset. M1 has just increased by $1000, and bank equity has (nominally) increased by $200. The loan, and the funding, are complete at this point. When you write a check that is deposited at a different bank, reserves (“hard” currency, liabilities of the central bank) are transferred from your bank’s reserve account to depositor’s bank’s reserve account, your account is marked down, and depositor’s account is marked up. This transaction is financially neutral for all parties.

This is where you will get an argument from fractional reserve people. Since the bank ends up transferring hard currency, isn’t this just a more complicated way to describe FR banking? Well, no. The bank didn’t need to collect reserves before making the loan; reserve requirements are calculated days after the loan was made. Also, the central bank will always supply enough reserves to banks, so hard currency isn’t a limiting factor. Finally, if you picture two banks, each creating identical loans that get deposited in the other bank, no reserves will be transferred, yet $2000 has still been created. Which is pretty much what happens on a large scale every day – the amount of loans created every day is far greater than the net amount of reserves that must be transferred in settlement at the end of the day. In our credit creation system, reserves are merely settlement funds. If you dissolved the central bank/settlement agent tomorrow, banks could still operate just fine settling up among themselves, using mostly bank-created credit to do so. If things got really unbalanced, they could then settle up using other assets. No “hard currency” required for loans or transactions. The central bank is now merely a useful tool for settlement, funding government spending, and backstopping banks in crisis.

This paper by Richard Werner explains the three theories of banking in good detail:

The Bank of England's paper on the subject, is a more technical read.