To protect the identity of the persons or firms on a microdata file, noise is sometimes added to the data before releasing it to the public. There has been conjecture that, rather than adding noise, multiplying noise might better protect the confidentiality. Two forms of multiplicative noise are considered. The first approach is generating random numbers which have mean one and small variance, and multiplying the original data by the noise. The second approach is to take a logarithmic transformation, compute a covariance matrix of the transformed data, generate random number which follows mean zero and variance/covariance c times the variance/covariance computed in the previous step, add the noise to the transformed data and take an antilog of the noise added data. This paper investigates the statistical properties of both methods and shows how well they protect the identity of those on the file via re-identification trials.