Figure 1-2.-2-percent grade.
In connection with the study of decimal
fractions, businessmen as early as the fifteenth
century made use of certain decimal fractions so
much that they gave them the special designation
PERCENT. The word percent is derived from
Latin. It was originally per centum, which means
by the hundredths. In banking, interest rates
are always expressed in percent; statisticians use
percent; in fact, people in almost all walks of life
use percent to indicate increases or decreases in
production, population, cost of living, and so on.
The Engineering Aid uses percent to express
change in grade (slope), as shown in figure 1-2.
Percent is also used in earthwork computations,
progress reports, and other graphical representa-
tions. Study chapter 6 of NAVEDTRA 1-0069-D1
for a clear understanding of percentage.
POWERS, ROOTS, EXPONENTS,
Any number is a higher power of a given root.
To raise a number to a power means to multiply,
using the number as a factor as many times as the
power indicates. A particular power is indicated
by a small numeral called the EXPONENT;
for example, the small 2 on 32 is an exponent
indicating the power.
Many formulas require the power or roots of
a number. When an exponent occurs, it must
always be written unless its value is 1.
A particular ROOT is indicated by the radical
sign (~), together with a small number called the
INDEX of the root. The number under the radical
sign is called the RADICAND. When the radical
sign is used alone, it is generally understood to
mean a square root, and ~, ~, and ~,
indicate cube, fifth, and seventh roots, respec-
tively. The square root of a number may be either
+ or . The square root of 36 may be written
thus: G = t6, since 36 could have been the
product of ( + 6)( + 6) or ( 6)( 6). However, in
practice, it is more convenient to disregard
the double sign ( ± ). This example is what we
call the root of a perfect square. Sometimes
it is easier to extract part of a root only
after separation of the factors of the number, such
as: ~ = ~ = 3~. As you can see, we
were able to extract only the square root
of 9, and 3 remains in the radical because
it is an irrational factor. This simplification
of the radical makes the solution easier because
you will be dealing with perfect squares and
Radicals are multiplied or divided directly.
Like fractions, radicals can be added or sub-
tracted only if they are similar.
When you encounter a fraction under the
radical, you have to RATIONALIZE the
denominator before performing the indicated
operation. If you multiply the numerator and
denominator by the same number, you can