Since we are talking dollars here, and not Euros or some other fiat...
I think if you research it you will find that the formal national debt of the United states is around $17 trillion, and increasing. I say United States because the dollar is associated with the United States, formally.
Part of the way that fiat money works is that, for every debit somewhere, there needs to be a credit. What this means is that for there to be a debt, a debit, there needs to be someone who owns the debt - that is, a credit(or), a credit. This means that there has to be with regard to the United States, at least $17 trillion dollars sitting around somewhere.
The U.S. Dollar remains the main fiat money of the world, even though other fiats and other actual valuables are traded as money here and there around the world. I think that if you research it, you will find that there is something like $200 trillion worth of U.S. Dollar debt in existence around the world. This means that there also needs to be $200 hundred trillion dollars worth of credit in existence. NOTICE THIS. It is only debit/credit using the Dollar as a measurement of the amount of debit/credit. It is NOT Dollars at all! even though we call it dollars.
Now, by far the largest amount of this debit/credit, U.S. Dollar money has not been printed. It is simply entries in ledgers in the banking system and elsewhere. Yet, if the system collapsed today for one reason or another, what MIGHT the value comparison between Bitcoin and the Dollar be. Simple math would suggest that something like $9.5 million to the Bitcoin ($200 trillion divided by 21 million), BUT ONLY IF Bitcoin happened to take over as the world's currency.
Why is the collapse of all fiat money imminent? Because, as has been stated above, fiat is NOT MONEY. It is simply an exchange of debit and credit when people and businesses of the world trade real materials. In other words, fiat is simply using make-believe-debts to trade for REAL goods, materials and labor. When the people realize this, they will collapse the fiat systems, because they will also realize that all the trading that they do involves handing a portion of the trades over to the bankers, increasing the bankers' wealth for nothing in return.
The question is, when this happens - fiat collapse - will Bitcoin survive? Or will people go back on the gold and silver systems? Or will there be something else? Remember, unlike gold and silver, Bitcoin could collapse with a collapse of the Internet or the power grid. And like gold and silver, you can't eat bitcoins.
Bitcoin will probably never approach $1,000,000,000 per Bitcoin. But it just might outlast the Dollar when the fiats all crash. But you never know. When fiats are about to crash, banks might make gigantic ledger entries in a last-ditch attempt to stall the crash.