Geoscience Reference
In-Depth Information
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Introduction
I thought I was mathematically dysfunctional. But I am not unique—69 out of every 9 people are also
dysfunctional.
—Frank R. Spellman (2005)
1.1 SETTING THE STAGE
It is general knowledge that mathematics is the study of numbers and counting and measuring, but
its associated collaterals are less recognized. Simply, mathematics is more than numbers; it also
involves the study of number patterns and relationships. It is also a means of communicating ideas.
Perhaps, however, mathematics, more than anything, is a way of reasoning that is unique to human
beings. No matter how we describe or define mathematics, one thing is certain—without an under-
standing of mathematical units and conversion factors, one might as well delve into the mysteries of
deciphering hieroglyphics while blindfolded and lacking the sense of touch and reason.
1.2 SI UNITS
The units most commonly used by environmental engineering professionals are based on the com-
plicated English system of weights and measures; however, bench work is usually based on the
metric system, or International System of Units (SI), due to the convenient relationship between mil-
liliters (mL), cubic centimeters (cm 3 ), and grams (g). The SI is a modernized version of the metric
system established by international agreement. The metric system of measurement was developed
during the French Revolution and was first promoted in the United States in 1866. In 1902, proposed
congressional legislation requiring the U.S. government to use the metric system exclusively was
defeated by a single vote. Although we use both systems in this text, the SI provides a logical and
interconnected framework for all measurements in engineering, science, industry, and commerce.
The metric system is much simpler to use than the existing English system, because all of its units
of measurement are divisible by 10.
Before listing the various conversion factors commonly used in environmental engineering it is
important to describe the prefixes commonly used in the SI system. These prefixes are based on the
power of 10. For example, a “kilo” means 1000 grams, and a “centimeter” means 1/100 of 1 meter.
The 20 SI prefixes used to form decimal multiples and submultiples of SI units are given in Table
1.1. Multiple prefixes may not be used. The prefix names shown in Table 1.1 are combined with the
unit name “gram,” and the prefix symbols are used with the unit symbol “g.” With this exception,
any SI prefix may be used with any SI unit, including the degree Celsius and its symbol °C.
EXAMPLE 1.1
10 -6 kg = 1 mg (one milligram) is acceptable, but not 10 -6 kg = 1 µkg (one microkilogram).
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