We enumerate the round-off errors in fixed point multiplication both for rounding by chopping and for symmetric rounding. Then we compute the mean and variance of the round-off error. For symmetric rounding, the formulas differ for an odd base β vs an even base β. We conclude that if symmetric rounding is to be used, there is an advantage to an odd base over an even base. For prime base β, no special assumption is needed. For non-prime base β, the last non-zero element of the first factor is assumed to be relatively prime to β.