Rounding error is an important source of measurement error that is common in index data. The problem can be traced to rounding that occurs to limit the number of digits after the decimal place to be reported in rebased index data. Rounding error introduces distortions that affect variance properties, alter the lag distributions of time series models, and cause a systematic bias in estimated coefficients. For instance, spuriously choppy inflation rates are obtained when constructed using the official CPI, rebased with 1982-84 = 100. Fortunately, the distortions can be generally avoided by using versions of data that have greater precision.