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How big?

How big? . How small?. Significant Digits and Isotopic Abundance. How accurate? . Reminder: bring a calculator to class. Scientific notation. Read “Scientific Notation” on page 621 Complete the chart below. Decimal notation. Scientific notation. 127.

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How big?

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  1. How big? How small? Significant Digits and Isotopic Abundance How accurate?

  2. Reminder: bring a calculator to class

  3. Scientific notation • Read “Scientific Notation” on page 621 • Complete the chart below Decimal notation Scientific notation 127 1.27 x 102 0.0907 9.07 x 10–2 0.000506 5.06 x 10–4 2 300 000 000 000 2.3 x 1012

  4. What time is it? • Someone might say “1:30” or “1:28” or “1:27:55” • Each is appropriate for a different situation • In science we describe a value as having a certain number of “significant digits” • The # of significant digits in a value includes all digits that are certain and one that is uncertain • “1:30” likely has 2, 1:28 has 3, 1:27:55 has 5 • There are rules that dictate the # of significant digits in a value (read handout up to A. Try A.)

  5. Answers to question A) 3 4 3 2 1 4 4 6 infinite 5 • 2.83 • 36.77 • 14.0 • 0.0033 • 0.02 • 0.2410 • 2.350 x 10–2 • 1.00009 • 3 • 0.0056040

  6. Note that a line overtop of a number indicates that it repeats indefinitely. E.g. 9.6 = 9.6666… • Similarly, 6.54 = 6.545454… Significant Digits • It is better to represent 100 as 1.00 x 102 • Alternatively you can underline the position of the last significant digit. E.g. 100. • This is especially useful when doing a long calculation or for recording experimental results • Don’t round your answer until the last step in a calculation.

  7. Adding with Significant Digits • Howfaris it fromToronto to room 229? To 225? • Adding a value that is much smaller than the last sig. digit of another value is irrelevant • When adding or subtracting, the # of sig. digits is determined by the sig. digit furthest to the left when #s are aligned according to their decimal.

  8. Adding with Significant Digits • Howfaris it fromToronto to room 229? To 225? • Adding a value that is much smaller than the last sig. digit of another value is irrelevant • When adding or subtracting, the # of sig. digits is determined by the sig. digit furthest to the left when #s are aligned according to their decimal. • E.g. a) 13.64 + 0.075 + 67 b) 267.8 – 9.36 13.64 267.8 + 0.075 – 9.36 + 67. 80.715 81 258.44 • Try question B on the handout

  9. i) ii) iii) 83.25 4.02 0.2983 – 0.1075 + 0.001 + 1.52 B) Answers 83.14 4.02 1.82

  10. Multiplication and Division • Determining sig. digits for questions involving multiplication and division is slightly different • For these problems, your answer will have the same number of significant digits as the value with the fewest number of significant digits. • E.g. a) 608.3 x 3.45 b) 4.8  392 a) 3.45 has 3 sig. digits, so the answer will as well 608.3 x 3.45 = 2098.635 = 2.10 x 103 b) 4.8 has 2 sig. digits, so the answer will as well 4.8  392 = 0.012245 = 0.012 or 1.2 x 10–2 • Try question C and D on the handout (recall: for long questions, don’t round until the end)

  11. i) 7.255  81.334 = 0.08920 ii) 1.142 x 0.002 = 0.002 iii) 31.22 x 9.8 = 3.1 x 102 (or 310 or 305.956) i) 6.12 x 3.734 + 16.1  2.3 22.85208 + 7.0 = 29.9 iii) 1700 ii) 0.0030 + 0.02 = 0.02 + 134000 iv) 33.4 135700 =1.36 x105 + 112.7 + 0.032 146.132  6.487 = 22.5268 = 22.53 C), D) Answers Note: 146.1  6.487 = 22.522 = 22.52

  12. Unit conversions • Sometimes it is more convenient to express a value in different units. • When units change, basically the number of significant digits does not. E.g. 1.23 m = 123 cm = 1230 mm = 0.00123 km • Notice that these all have 3 significant digits • This should make sense mathematically since you are multiplying or dividing by a term that has an infinite number of significant digits E.g. 123 cm x 10 mm / cm = 1230 mm • Try question E on the handout

  13. i) 1.0 cm = 0.010 m ii) 0.0390 kg = 39.0 g iii) 1.7 m = 1700 mm or 1.7 x 103 mm E) Answers

  14. Isotopic abundance • Read 163 – 165 • Let’s consider the following question: if 12C makes up 98.89% of C, and 13C is 1.11%, calculate the average atomic mass of C: Mass from 12C atoms + Mass from 13C atoms 12 x 0.9889 13 x 0.0111 + = 12.01 11.8668 + 0.1443 • To quickly check your work, ensure that the final mass fits between the masses of the 2 isotopes • Do the sample problem (page 165) as above and try questions 10 and 11 (page 166)

  15. Mass from 35Cl + Mass from 37Cl 35 x 0.7553 37 x 0.2447 + 26.4355 + 9.0539 Mass from 39K + Mass from 41K 39 x 0.9310 41 x 0.0690 + 36.309 + 2.829 + Mass from 38Ar Mass from 40Ar + Mass from 36Ar 38 x 0.0006 40 x 0.9960 36 x 0.0034 + + + 0.0228 39.84 + 0.1224 Isotopic abundance = 35.49 = 39.14 = 39.99

  16. More practice • Answer questions 1 – 3 on page 179. Your answers should have the correct number of significant digits. For more lessons, visit www.chalkbored.com

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