Your explanation doesn't make sense. If you actually do look at what happened with the inflationary dollar since the "late 19th century", it lost 96-97% of its purchasing power due to the monetary inflation.
Which means that if your grandma stored her wealth in dollars and wanted to pass it onto you, you can only enjoy 3-4% of what's left.
http://4.bp.blogspot.com/-YTyPGaEsBcw/T0Kd1nS9zJI/AAAAAAAABQ...