Financial Prices are often discretized-to the nearest cent, for example.Thus we can say prices are observed with rounding errors.Rounding errors affect the estimation of volatility and understanding them becomes important especially when we use High-Frequency Data.We discuss different models involving rounding, in eluding "small" rounding, pure rounding with a fixed rounding level, and rounding combined with random error.Asymptotic theorems for each of these are derived.And simulation results are shown.This talk is based on joint work with Per A.Mykland.