°°° ALGEBRAIC OPERATIONS Here's a mnemonic sentence for the order or sequence in which operations are carried out in algebraic and numerical expressions: " Bless My Dear Aunt Sally! " (Brackets, Multiplications, Divisions, Additions, Subtractions) Thus (3*4+4/2-3)*5 is calculated in steps as: calculate for brackets first = [3*4+4/2-3] [*5] multiply within, then divide = [12+2-3] [*5] add within, then subtract = [11] [*5] = 55 Those who use the term "parentheses" instead of "brackets" may prefer to "Please My Dear Old Sally". "Extra" brackets or parentheses may be written in for clarity (ie. [[3*4]+[4/2]-2]*5 ), but computer programmers write only the pared-down versions of formulas wherever possible in order to save on computer calculation run-times. Bruce Nerve of Manchester NH(USA) sent us an alternative (in Apr/00) that expands the mnemonic to include exponents (being quantities of power or indices, such as 32): " Please Excuse My Dear Aunt Sally! " (Parentheses, Exponents, Multiplications, Divisions, Additions, Subtractions) Exponents are also used in "floating point" representation. A floating point number is usually written in the form a x rn, where a is called a mantissa, and r is the number base (ie. 10 for decimal, 2 for binary etc), and n is an integer called the exponent. Thus for example 2 x 10 4 = 20,000 (the point being shifted 4 places to the right) and 2 x 10 -4 = 0.0002 (the minus indicating 4 places to the left). Decimal numbers are sometimes written exponentially as aEn, whereby 2E04 means 2 x 10 4 = 20,000. Incidentally the exponent sign E should not be confused with Euler's Constant sign e (used as the base of natural logarithms).

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