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Negative numbers are preceded by a minus sign. Although the physical
quantities used in biomechanics do not have values that are less
than zero in magnitude, the minus sign is often used to indicate
the direction opposite the direction regarded as positive. Therefore,
it is important to recall the following rules regarding arithmetic
operations involving negative numbers:
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1. Addition of a negative number yields the same results
as subtraction of a positive number of the same magnitude:
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2. Subtraction of a negative number yields the same
result as addition of a positive number of the same magnitude:
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3. Multiplication or division of a number by a number
of the opposite sign yields a negative result:
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4. Multiplication or division of a number by a number
of the same sign (positive or negative) yields a positive result:
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Exponents are superscript numbers that immediately follow a base
number, indicating how many times that number is to be self-multiplied
to yield the result:
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Taking the square root of a number is the inverse operation of
squaring a number (multiplying a number by itself). The square root
of a number is the number that yields the original number when multiplied
by itself. The square root of 25 is 5, and the square root of 9
is 3. Using mathematics notation, these relationships are expressed
as the following:
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Because −5 multiplied by itself also equals
25, −5 is also a square root of 25. The following
notation is sometimes used to indicate that square roots may be
either positive or negative:
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When a computation involves more than a single operation, a set
of rules must be used to arrive at the correct result. These rules
may be summarized as follows:
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1. Addition and subtraction are of equal precedence;
these operations are carried out from left to right as they occur in
an equation:
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2. Multiplication and division are of equal precedence;
these operations are carried out from left to right as they occur
in an equation:
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3. Multiplication and division take precedence over
addition and subtraction. In computations involving some combination
of operations not of the same level of precedence, multiplication
and division are carried out before addition and subtraction are
carried out:
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4. When parentheses (), brackets [ ],
or braces { } are used, the operations enclosed
are performed first, before the other rules of precedence are applied:
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Simple computations in biomechanics problems are often performed
quickly and easily with a hand-held calculator. However, the correct
result can be obtained on a calculator only when the computation
is set up properly and the rules for ordering ...