  In a recent paper, a "distance" function, \cal D, was defined which measures
the distance between pure classical and quantum systems. In this work, we
present a new definition of a "distance", D, which measures the distance
between either pure or impure classical and quantum states. We also compare the
new distance formula with the previous formula, when the latter is applicable.
To illustrate these distances, we have used 2 \times 2 matrix examples and
2-dimensional vectors for simplicity and clarity. Several specific examples are
calculated.
