Quantum Physics

A.2 Appendix A Mathematical Reviewand so on. The number of zeros corresponds to the power to which 10 is raised,called the exponent of 10. For example, the speed of light, 300 000 000 m/s, canbe expressed as 3 10 8 m/s.For numbers less than one, we note the following:10 1 1 10 0.110 2 10 3 10 4 10 5 110 10 0.01110 10 10 0.001110 10 10 10 0.000 1110 10 10 10 10In these cases, the number of places the decimal point is to the left of the digit 1equals the value of the (negative) exponent. Numbers that are expressed as somepower of 10 multiplied by another number between 1 and 10 are said to be inscientific notation. For example, the scientific notation for 5 943 000 000 is5.943 10 9 and that for 0.000 083 2 is 8.32 10 5 .When numbers expressed in scientific notation are being multiplied, the followinggeneral rule is very useful:10 n 10 m 10 nm [A.1]where n and m can be any numbers (not necessarily integers). For example,10 2 10 5 10 7 . The rule also applies if one of the exponents is negative. For example,10 3 10 8 10 5 .When dividing numbers expressed in scientific notation, note that10 n10 m 10n 10 m 10 nm 0.000 01EXERCISESWith help from the above rules, verify the answers to the following:1. 86 400 8.64 10 42. 9 816 762.5 9.816 762 5 10 63. 0.000 000 039 8 3.98 10 84. (4.0 10 8 )(9.0 10 9 ) 3.6 10 185. (3.0 10 7 )(6.0 10 12 ) 1.8 10 475 10 116.5.0 103 1.5 107(3 10 6 )(8 10 2 )7.(2 10 17 )(6 10 5 ) 2 1018[A.2]A.3 ALGEBRAA. Some Basic RulesWhen algebraic operations are performed, the laws of arithmetic apply. Symbolssuch as x, y, and z are frequently used to represent quantities that are not specified,what are called the unknowns.First, consider the equation8x 32If we wish to solve for x, we can divide (or multiply) each side of the equation bythe same factor without destroying the equality. In this case, if we divide both sides