Dave Gerr - Boat Mechanical Systems Handbook-How to Design, Install, and Recognize Proper Systems in Boats

xix

USING DECIMAL

EXPONENTS

Decimal exponents are used in a number of
the formulas throughout this book. If you
“don’t like math,” decimal exponents can
seem a bit technical. Don’t let them put you
off, however. Decimal exponents are easy to
master; it takes just a few moments. For
instance, in the formula for BBB chain
weight, Formula 24-4,

BBB chain weight, lb./ft. ≈10.505 ×

(chain dia., in.)1.858

1.858 is the decimal exponent.
It’s quite easy to solve this on a pocket sci-
entific calculator (an inexpensive one from
any local stationery store or RadioShack), but
it’s important to understand what decimal
exponents are

as^3 Xor the cube root of X

as X or X , the square root of X^2

as (X× X ) or X times the square root of X

same as (X ) orX squared times

the cube

(^2) × (^3) X
rroot of X
and so on.
You can see that a decimal is just another
way of writing a fraction and that it makes no
difference whether you use a decimal or a
fraction as the exponent. (The decimal, of
course, is easier to enter in a calculator.)
You can also see that a decimal or frac-
tional exponent is the same as taking the root
of a number, and the root is always the same as
the inverse (or reciprocal) of the decimal.
Thus, raising a number to the 0.5 power is the
same as taking the square root of that number.
(The inverse or reciprocal of 0.5 = 1 ÷ 0.5 = 2,
and is the same as .) Raising a num-
ber to the 0.333 power is the same as taking the
cube root of that number. (The reciprocal of
0.333 = 1 ÷ 0.333 = 3, giving .)
The nice thing about decimal exponents is
that they allow quick manipulation of formu-
las with exponential relationships that don’t
(^3) X

X^2 X

Author’s Notes

X0.5is the same as X^1 /^2 is the same

X0.333is the same as X^1 /^3 is the same

X1.5is the same as X ×X^1 /^2 is the same

X2.333is the same as X^2 ×X^1 /^3 is the same