Introduction - Basic Mathematics for Water and Wastewater Operators - page 4

There can be little doubt that the proper use of a calculator can reduce the time
and effort required to perform calculations; thus, it is important to recognize the
calculator as a helpful tool, with the help of a well-illustrated instruction manual, of
course. The manual should be large enough to read, not an inch by an inch by a quar-
ter of an inch in size. It should have examples of problems and answers with illustra-
tions. Careful review of the instructions and working through example problems are
the best ways to learn how to use the calculator.
Keep in mind that the calculator you select should be large enough so that you can
use it. Many of the modern calculators have keys so small that it is almost impossible
to hit just one key. You will be doing a considerable amount of work during this study
effort—make it as easy on yourself as you can.
Another significant point to keep in mind when selecting a calculator is the
importance of purchasing a unit that has the functions you need. Although a cal-
culator with a lot of functions may look impressive, it can be complicated to use.
Generally, the wastewater plant operator requires a calculator that can add, subtract,
multiply, and divide. A calculator with a parentheses function is helpful, and, if you
must calculate geometric means for fecal coliform reporting, logarithmic capability
is helpful.
In many cases, calculators can be used to perform several mathematical functions
in succession. Because various calculators are designed using different operating
systems, you must review the instructions carefully to determine how to make the
best use of the system.
Finally, it is important to keep a couple of basic rules in mind when performing
calculations:

• Always write down the calculations you wish to perform.

• Remove any parentheses or brackets by performing the calculations inside

first.

DIMENSIONAL ANALYSIS
Dimensional analysis is a problem-solving method that uses the fact that any number
or expression can be multiplied by 1 without changing its value. It is a useful tech-
nique used to check if a problem is set up correctly. In using dimensional analysis to
check a math setup, we work with the dimensions (units of measure) only—not with
numbers. To use the dimensional analysis method, we must know how to perform
three basic operations. Unit factors may be made from any two terms that describe
the same or equivalent amounts of what we are interested in; for example, we know
that 1 inch = 2.54 centimeters.

B asiC o peration 1
To complete a division of units, always ensure that all units are written in the same
format; it is best to express a horizontal fraction (such as gal/ft 2 ) as a vertical fraction :