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Homework 2.1 – Due Wednesday 9/3/14 Chapter 2 #s 1, 2, 4, 8-28 (even), 32, 34, 80, 86, 88

Happy Birthday Lyndon Johnson (1908). Homework 2.1 – Due Wednesday 9/3/14 Chapter 2 #s 1, 2, 4, 8-28 (even), 32, 34, 80, 86, 88 Homework 2.2 – Due Wednesday 9/10/14 Chapter 2 #s 38-48 (even), 56-76 (even), 84, 92, 94 Lab Next Week. Significant Figures.

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Homework 2.1 – Due Wednesday 9/3/14 Chapter 2 #s 1, 2, 4, 8-28 (even), 32, 34, 80, 86, 88

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  1. Happy Birthday Lyndon Johnson (1908) • Homework 2.1 – Due Wednesday 9/3/14 • Chapter 2 #s 1, 2, 4, 8-28 (even), 32, 34, 80, 86, 88 • Homework 2.2 – Due Wednesday 9/10/14 • Chapter 2 #s 38-48 (even), 56-76 (even), 84, 92, 94 • Lab Next Week

  2. Significant Figures • Significant figures tell you about the uncertainty in a measurement. • Significant figures include all CERTAIN (known) digits, and ONE UNCERTAIN (guessed) digit 11.84 cm 4 significant figures

  3. Significant Figures • Significant figures include all CERTAIN (known) digits, and ONE UNCERTAIN (guessed) digit 520 cm 2 significant figures

  4. How many Sig. Figs.? Two rules: • #1) If there IS a decimal point in the number: • Start at right of number and count until the LAST non-zero digit

  5. How many Sig. Figs.? Two rules: • #1) If there IS a decimal point in the number: • Start at right of number and count until the LAST non-zero digit • #2) If there is NOT a decimal point in the number • Start at left of number and count until the LAST non-zero digit

  6. How many Sig. Figs.? 2 3 . 0 0 2 8 0 1 0 9 significant figures 0 . 0 6 8 0 0 4 significant figures 1 0 0 . 0 0 0 6 significant figures

  7. How many Sig. Figs.? 7 4 2 9 3 5 significant figures 2 3 0 8 0 0 4 significant figures 1 0 0 0 0 0 1 significant figure

  8. 60020300 12.00500 0.0005 0.10046 6 s.f. 7 s.f. 1 s.f. 5 s.f. Significant Practice 320000 8900. 0.0061000 0.1528 2 s.f. 4 s.f. 5 s.f. 4 s.f.

  9. Rounding Numbers • Find the last significant digit. • If the next digit to the right is 4 or less, leave the last significant digit alone. • If the next digit to the right is 5 or more, round the last significant digit up.

  10. 0.00259428 (3 s.f.) = 0.00259 0.00259428 (3 s.f.) 54.3675701 (5 s.f.) = 54.368 54.3675701 (5 s.f.) 8265391000 (2 s.f.) = 8300000000 8265391000 (2 s.f.) 0.1659822 (4 s.f.) = 0.166 = 0.1660 0.1659822 (4 s.f.) 0.0005473300 (5 s.f.) = 0.00054733 0.0005473300 (5 s.f.) 2617890100 (6 s.f.) = 2617890000 2617890100 (6 s.f.)

  11. Sig. Figs. in Calculations Two rules: • #1) Multiplication and Division • The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer.

  12. Calculations with Sig. Figs. • Multiplication and division • The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer. 1.5 x 7.3254 = 1 0 .9881 = 11 2 s.f. 5 s.f.

  13. Calculations with Sig. Figs. • Multiplication and division • The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer. 6.127 x 0.0000267030 = 0.000163 6 09 = 0.0001636 4 s.f. 6 s.f.

  14. Calculations with Sig. Figs. 927.381 / 456.0 = 2.03 3 730263 = 2.034 6 s.f. 4 s.f.

  15. Calculations with Sig. Figs. 0.00159 / 2 = 0.000 7 95 = 0.0008 3 s.f. 1 s.f.

  16. Calculations with Sig. Figs. 6 s.f. 3 s.f. = 18 8 99522.37 = 18900000 4 s.f.

  17. 890.00 x 112.3 78132/2.50 0.0120 x 48.15 x 0.0087 Some Practice 500 x 0.000230012

  18. 890.00 x 112.3 78132/2.50 0.0120 x 48.15 x 0.0087 99950 31300 0.0050 Some Practice

  19. 500 x 0.000230012 0.000000025 1900000 0.1 Some Practice

  20. Sig. Figs. in Calculations Two rules: • #1) Multiplication and Division: • The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer. • #2) Addition and Subtraction: • The value in the calculation that has the FEWEST decimal spots determines the number of decimal spots in your answer.

  21. Adding and subtracting with sig. figs. 0.0025647 + 0.000321 7 decimal places 6 decimal places 0.0025647 0.0025647 +0.000321_ +0.000321_ 0.0028857 0.0028857 = 0.002886 answer can only be precise to the 6th decimal place

  22. Adding and subtracting with sig. figs. 394.0150 + 0.0074121 4 decimal places 7 decimal places 394.0150 394.0150 +0.0074121 + 0.0074121 394.0224121 394.0224121 = 394.0224 answer can only have 4 decimal places

  23. Adding and subtracting with sig. figs. 682300 + 5922.60 precise to the hundreds place precise to the 2nd decimal spot 682300 682300 + 5922.60 + 5922.60 NO!!!! 688222.60 688222.60 = 6882 688200 answer must have the same precision as the least precise measurement (the hundreds place)

  24. 23.67 – 75 5502.8 + 24.691 + 0.01 0.109 + 0.09 – 0.955 20.4 + 1.322 + 78 0.000004 + 11.23115 5449000 + 162211 -51 5527.5 -0.76 100. 11.23115 5611000 Some More Practice

  25. Scientific Notation – Numbers > 1 Place a decimal so that there is a single digit to the left 1.8900000 18900000 Start counting from the right until you get to the decimal 1. 8 9 0 0 0 0 0 7 6 5 4 3 2 1 This becomes the exponent for “times 10 to the” 1.8900000x107 Remove digits from the right until proper # of sig. figs. 1.8900000x107 1.890000x107 1.89000x107 1.8900x107 1.890x107 1.89x107

  26. Scientific Notation – Numbers > 1 Place a decimal so that there is a single digit to the left 7.16110 716110 Start counting from the right until you get to the decimal 7. 1 6 1 1 0 5 4 3 2 1 This becomes the exponent for “times 10 to the” 7.16110x105 Remove digits from the right until proper # of sig. figs. 7.16110x105 7.1611x105 7.1611x105

  27. Scientific Notation – Numbers < 1 Start counting from the decimal point to the first non-zero digit. This will be the exponent in the “times ten to the negative” 0. 0 0 0 0 0 0 5 7022169 1 2 3 4 5 6 7 Move the decimal point to the right of the first non-zero digit, drop all of the leading zeros, and add the “times ten to the negative” with the exponent. 5.7022169x10-7

  28. Scientific Notation – Numbers < 1 Start counting from the decimal point to the first non-zero digit. This will be the exponent in the “times ten to the negative” 0. 0 0 0 0 9 510 1 2 3 4 5 Move the decimal point to the right of the first non-zero digit, drop all of the leading zeros, and add the “times ten to the negative” with the exponent. 9.510x10-5

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