Ch. 2 Math Review

1. Ch. 2 Math Review

2. Scientific Notation • Scientific Notation: a method for making small and large numbers more manageable to work with. • Moving the decimal to the right results in a negative exponent, to the left a positive exponent. • Move decimal so the first part of the number has one digit to the left of the decimal, all others after the decimal. Ex. 0.00527g = 5.27 x 10-3 g 52700000 m = 5.27 x 107 m 3.25 x 10-6 cm3 = 0.00000325 cm3 3.25 x 104 cm3 = 32500cm3 2-2

3. Scientific Notation • Practice: 1) 0.000060731 ml = 2) 2.970 x 10-5 mg = 3) 546901000 kg = 4) 6.3 x 107 s = 2-3

4. Rounding Atomic Masses • Rounding Atomic Masses: we will be rounding the atomic masses off the periodic table to the hundredths place. (2 numbers after the decimal point) Ex. C = 12.011 g/mol = 12.01 g/mol Bi = 208.98038 g/mol = 208.98 g/mol K = 39.0983 g/mol = 39.10 g/mol

5. Rounding Atomic Masses • Practice: 5) N = 14.00674 g/mol = 6) Si = 28.0855 g/mol = 7) O = 15.9994 g/mol = 8) Ar = 39.948 g/mol = 2-5

6. Significant Figures • Non zeros are always significant. • Zeros between non zeros are significant. • Leading and trailing zeros depend on the presence of a decimal. Atlantic/Pacific Rule: Pacific: Point Present, start from the left, first nonzero and everything after is significant Atlantic: Point Absent, start from the right, first nonzero and everything after is significant.

7. Significant Figures Ex. 1200 = 2 sig figs 0.003 = 1 sig fig 1.200 = 4 sig figs 0.0030 = 2 sig figs Practice: • 1.2650 = 10) 325000 = • 1.280 x 10-1 = 12) 31006 = 2-7

8. Significant Figures Rounding Calculations According to Sig Figs Addition and Subtraction: Round answers to the lowest place value of the numbers that you are working with: Ex. 2.2 6.9801 + 5.67 - 4.21 7.87 = 7.9 2.7701 = 2.77 2-8

9. Significant Figures Practice: • 4.71 - 1.1 • 5.367 + 1.2 2-9

10. Significant Figures • Multiplication and Division: Round answers to the least number of sig figs of the numbers that you are working with: Ex. 2.60 x 300 = 780 = 800 52.31 x 2600 = 136006 = 140000 2000000 ÷ 5.63 = 355239.7869 = 400000 78 ÷ 6 =13 = 10 2-10

11. Significant Figures Practice: • 240. ÷ 6.0 = • 365 ÷ 5 = • 32 ÷ 3 = • 32 x 3.0 = 2-11

12. Dimensional Analysis • Used to convert between units. Take an equivalent (12 in. = 1 ft.) and make it into a conversion factor: 1 ft. or 12 in. 12 in. 1 ft. Use conversion factors to convert between units. Always start with the number and units you are converting and multiply by the conversion factor with the starting units on the bottom. (so they cancel) 2-12

13. Dimensional Analysis • Ex. 5.36 ft. = ? in. 5.36 ft. x 12 in. = 64.32 in. = 64.3 in. 1 ft. • 32 in. = ? ft. 32 in. x 1 ft. = 2.666 ft. = 2.7 ft. 12 in. 12-13

14. Dimensional Analysis • Ex. 3.26 in. = ? cm 3.26 in. x 1 cm= 8.280416561 cm = 8.28 cm 0.39370 in. • 25 g = ? kg just use your handout, move your decimal 3 places to the left 25 g = 0.025 kg • 5.69 oz. = ? g 5.69 oz. x 28.3 g= 161.027 g = 161 g 1 oz.

15. Dimensional Analysis • Ex. 1 year = ? S 1 year x 365 days x 24 hours x 60 min. X 60 s = 1 yr. 1 day 1 hr. 1 min. = 31536000 s = 30000000 s 12-15