ARITHMETIC, POWERS, AND ROOTS

Arithmetic, Powers, and Roots CHAPTER 3 MATH FOR CIVIL SERVICE TESTS... 

The measurement error might be described by the mean error (arithmetic mean value), the variance of the error, but also by the mean square error, the mean error power, and the root mean square error. 

Scientific calculators will perform all of the arithmetic operations we have just described (as well as those discussed in the next section). On most calculators, the basic operations of addition, subtraction, multiplication, and division are similar and straightforward. However, more variation exists in raising a number to a power and extracting a root. If you have the calculator instructions, by aU means read them. Otherwise, the following information may help. 

The diametei of average mass and surface area are quantities that involve the size raised to a power, sometimes referred to as the moment, which is descriptive of the fact that the surface area is proportional to the square of the diameter, and the mass or volume of a particle is proportional to the cube of its diameter. These averages represent means as calculated from the different powers of the diameter and mathematically converted back to units of diameter by taking the root of the moment. It is not unusual for a polydispersed particle population to exhibit a diameter of average mass as being one or two orders of magnitude larger than the arithmetic mean of the diameters. In any size distribution, the relation ia equation 4 always holds. 

---