How do I change the base year from multiple years to one with monthly data? I have a Consumer Price Index series in monthly frequency from January 1947 to September 2017 with base year 1982-1984 (units are: Index 1982-1984=100), which, I think, means that the simple average of CPI values from January 1982 to December 1984 is equal to 100. I calculated the average of those monthly values and found that it is equal to 100.01667, which may be due to the rounding errors because the data are rounded to one decimal place. The problem is that I would like to have (still monthly) CPI with base year 2009, so that the average of its values in 2009 would be equal to 100, and I don't know how to do that. Does anyone have the idea how to shift a base year of those monthly data from 1982-1984 to 2009? It would be much appreciated. Thank you very much.
One possible approach


Take the average of the original values for the 12 months of 2009. Call this "the original 2009 average"
Divide all the original values by "the original 2009 average"
Multiply by 100
Round