Parenthesizing sign operators

The order of operations was covered in Chapter 3, Properties of Numbers. Be aware of some distinctions when working with the order of operations and exponents. Exponents are done after parentheses and before any other operations, including the negative sign. For example, -32 = -(3 x 3) = -9 because you first take the second power of three and then the answer is negative. However, (-3)2 = -3 x -3 = 9, since -3 is enclosed in parentheses. Following are some examples of order of operations with exponents. 

Mathematical operations have specific rules for the use of mathematical symbols with SI units. A space or a half-high dot represents the multiplication of units a negative exponent, horizontal line, or slash represents the division of units, and if these mathematical symbols appear in the same line, parentheses must differentiate them. The percent sign (%) denotes the number 0.01 or 1/100, so that 1%= 0.01, 30% = 0.30, and so forth. Arabic numerals with the appropriate SI or recognized unit indicate the values of quantities. Commas are not used to separate numbers into groups of three. If more than four digits appear on either side of the decimal point, a space Table 3. Prefixes. separates the groups of three. 

When an equation is too long to fit on one line, break it after an operator that is not within an enclosing mark (parentheses, brackets, or braces) or break it between sets of enclosing marks. Do not break equations after integral, product, and summation signs after trigonometric and other functions set in roman type or before derivatives. 

The two functions xj/s and have an important symmetry property. If we exchange the coordinates of electrons 1 and 2 (interchange the I s and 2 s in the parentheses), the function xj/s is unaffected xj/s is symmetric under this operation. The function xj/ changes sign under this operation and so is antisymmetric. 

In cell Dl, enter the label °F . In cell D2, type the formula = (9/5) B2+32 . This is equivalent to writing °F = (9/5) °C + 32. The slash (/) is a division sign and the asterisk ( ) is a multiplication sign. Parentheses are used to make the computer do what we intend. Operations inside parentheses are carried out before operations outside the parentheses. The computer responds to this formula by writing —328 in cell D2. This is the Fahrenheit equivalent to —200°C. Select cells D2 through D6. In the Home ribbon, go to Editing and select Fill and then Down to complete the table shown in Figure 3-3c. 

This means (Appendix 3) that functions of species Ag are even (gerade) under inversion, while A functions (changing sign) are odd (ungerade). The combinations of projection operator (A3.23). For example, the projector for species is E — i, and, referring to the transformation properties listed above, (E —i)2 — (a function of A symmetry). Thus we find (indicating S, M values in parentheses) ... 

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