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Use the Inflation Calculator of the Bureau of Labor Statistics.
The U.S. government's Bureau of Labor Statistics offers a handy inflation calculator. It is here:
It is based on the BLS's own estimate of the Consumer Price Index (CPI). It is therefore as close to an official index of the decline of the value of the dollar as there is.
It begins in 1913, the year before the Federal Reserve System went into opeartion.