Funny, I was thinking the exact opposite. The Mach number has two velocities that cancel out, and velocity tends to be an easy concept to grasp, making it a textbook example of a dimensionless number. The part where Mach numbers are converted back to velocities requires you to input knowledge on the speed of sound, but there isn't a single answer for that unless you know the composition of the fluid, which is dependent on chemical composition, altitude and temperature. If you take a guess for that number, it's a unit conversion error rather than a variation in the dimensionless quantity itself.