The Chemistry Maths Book, Second Edition

10 Chapter 1Numbers, variables, and units where 10 −n 1 = 11210 n and 10 0 1 = 11 (see Section 1.6). 0 Exercises 37–42 A number ...

1.4 Decimal representation of numbers 11 An irrational number cannot be represented exactly in terms of a finite number of digit ...

12 Chapter 1Numbers, variables, and units The Euler number e The number eis defined by the ‘infinite series’ (see Chapter 7) = 1 ...

1.5 Variables 13 A number whose exact (decimal) representation involves more than a given number of digits is reduced most simpl ...

14 Chapter 1Numbers, variables, and units EXAMPLE 1.11The spectrum of the hydrogen atom The energy levels of the hydrogen atom a ...

1.6 The algebra of real numbers 15 EXAMPLES 1.12Examples of the rules of arithmetic rule examples 1.a 1 + 1 b 1 = 1 b 1 + 1 a 21 ...

16 Chapter 1Numbers, variables, and units The index rule Numbers are often written in the form a m , where ais called the basean ...

1.6 The algebra of real numbers 17 11.(a m ) n 1 = 1 (a n ) m 1 = 1 a m×n (g) (2 2 ) 3 1 = 1 (2 2 ) 1 × 1 (2 2 ) 1 × 1 (2 2 ) 1 ...

18 Chapter 1Numbers, variables, and units with the parentheses indicating that the addition is to performed first, and 21 + 1 (3 ...

1.8 Units 19 What not to do:(a 1 + 1 b) n 1 ≠ 1 a n 1 + 1 b n , where ≠means ‘is not equal to’. Thus, in case (3): (2 1 + 1 3) 2 ...

20 Chapter 1Numbers, variables, and units 14 SI (Système International d’Unités) is the international standard for the construct ...

1.8 Units 21 Table 1.2 SI derived units with special names and symbols Physical quantity Name Symbol Description SI unit frequen ...

22 Chapter 1Numbers, variables, and units The standard acceleration of gravity isg 1 = 1 9.80665 m s − 2 1 = 1 980.665 Gal, wher ...

1.8 Units 23 as required. It follows that when equation (1.1) is written in the formV 1 = 1 nRT 2 p, as in Example 1.1, the dime ...

24 Chapter 1Numbers, variables, and units EXAMPLES 1.18Molecular properties: mass, length and moment of inertia (i)mass. Atomic ...

1.8 Units 25 EXAMPLES 1.19Molecular properties: wavelength, frequency, and energy The wavelength λand frequency νof electromagne ...

26 Chapter 1Numbers, variables, and units This has dimensions of inverse length and is normally reported in units of the recipro ...

1.8 Units 27 Atomic units The equations of motion in quantum mechanics are complicated by the presence of the physical quantitie ...

28 Chapter 1Numbers, variables, and units In this form the equation is often referred to as the ‘Schrödinger equation in atomic ...

1.9 Exercises 29 1.9 Exercises Section 1.2 Calculate and express each result in its simplest form: 31 + 1 (−4) 2. 31 − 1 (−4) ...