The result is this: for every $1 the Fed creates, banks loan (up to) 0.91 + 0.92 + 0.93 + ... = $9
Please explain how come a $1 bill becomes $9 if you just take it out from your pocket and put it back into your pocket 9 times
It's not magic. It is called "fractional reserve banking" and it works like this:
Bank A has $1.
Bank A loans $0.90 to a customer who buys from merchant B, who deposits the money in bank B. Merchant B believes he has $0.90.
Bank B loans $0.81 to a customer who buys from merchant C, who deposits the money at bank C. Merchant C believes he has $0.81.
Bank C loans $0.73 to a customer who buys from merchant D, who deposits the money at bank D. Merchant D believes he has $0.73.
Bank D loans $0.66 to a customer who buys from merchant E, who deposits the money at bank E. Merchant E believes he has $0.66.
Bank E loans $0.59 to a customer who buys from merchant F, who deposits the money at bank F. Merchant F believes he has $0.59.
Bank F loans $0.53 to a customer who buys from merchant G, who deposits the money at bank G. Merchant G believes he has $0.53.
Bank G loans $0.48 to a customer who buys from merchant H, who deposits the money at bank H. Merchant H believes he has $0.48.
Bank H loans $0.43 to a customer who buys from merchant I, who deposits the money at bank I. Merchant I believes he has $0.43.
Bank I loans $0.39 to a customer who buys from merchant J, who deposits the money at bank J. Merchant J believes he has $0.39.
...
In the end, there is actually only $1 split among a large number of banks, but each depositor believes that they have the amount that they deposited and the fact that the depositors can withdraw their deposits at any time confirms it (as long as all depositors don't withdraw at the same time). The total amount of deposits is $9, so even though there is only 1 physical dollar, there are 9 additional virtual dollars which are nearly indistinguishable from the original $1.