I don't think any of the answers given so far are the reason there's not rampant inflation.
The reason is that the fed offers a competitive interest rate on excess reserves to serve as a magnet to "suck" all the new money back onto its own balance sheets as soon as the bond purchases are made, so that it doesn't get out into the economy.
Look - all the money (mainly in the form of US T-Bonds), is sitting backed up on the feds balance sheet...
http://qz.com/157198/the-federal-reserves-balance-sheet-will-hit-a-mind-boggling-4-trillion-any-day-now/Read this wiki article which states how the law was changed in 2008 to allow the fed to do this. The express purpose was so that they could start doing QE without it causing rampant inflation.
http://en.wikipedia.org/wiki/Excess_reserves#In_the_United_States_.282008-.29(Actually, this poster is saying the same thing)
When we say the govt is printing money, we are not really talking about the paper notes in circulation, rather electronic money (digits in a computer screen) that exists in bank accounts.
Yes, of course. They are not doing that either though.
an excerpt from some quick google search result:
When the Fed creates $85 billion, it uses this money to buy bonds - typically split 50/50 between US Treasuries and Mortgage Backed Securities (MBS). Here is what's important: When the Fed creates and gives $85 billion in reserves to its member banks, it removes $85 billion worth of assets (bonds) from the balance sheets of those same member banks. The result is that no new net financial assets enter the economy.