In 1803 the US paid $15 million for the Louisiana Purchase (white part in map below). Today this would be closer to $15 trillion. So maybe a factor of 1 million inflation.
By official inflation numbers this $15 million is $236 million in 2014 U.S. dollars. This is about a factor of 16 inflation.
Originally the dollar was defined as 1 oz of silver. Now silver is about $16 dollars/oz, or a factor of 16 inflation.
Gross public debt in 1800 was $83 million. Today gross public debt is $21.7 trillion. This is a factor of 261,000.
It is interesting that silver is only up by a factor of 16 and public debt is up by a factor of 261,000.
This reminds me of a movie where Dr Evil, who was frozen in the 1960s and then woken up in the present, threatens the world with nukes and demands "1 million dollars". In the early 1960s they still had real silver dollars in circulation.