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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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Addition of a negative number yields the same results as subtraction of a positive number of the same magnitude:
Subtraction of a negative number yields the same result as addition of a positive number of the same magnitude:
Multiplication or division of a number by a number of the opposite sign yields a negative result:
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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Addition and subtraction are of equal precedence; these operations are carried out from left to right as they occur in an equation:
Multiplication and division are of equal precedence; these operations are carried out from left to right as they occur in an equation:
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:
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 handheld calculator. However, the correct result can be obtained on a calculator only when the computation is set up properly and the rules for ordering of operations are followed. Most ...