The purpose of this article is to show how index numbers are being systematically distorted by significant rounding errors in the revised or rebased data. After a brief discussion of why index numbers are especially vulnerable to rounding errors, the CPI for urban wage earners and clerical workers (CPI-W) is used to illustrate how large these errors can be and how they now distort the pattern of monthly changes in the 1960s. Next, a Monte Carlo study is presented to show some of the econometric problems associated with rounding errors of this magnitude. Finally, I recommend steps to better understand and/or alleviate this problem.