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How big?

How big?. How small?. Significant Digits. 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. 1.27 x 10 2. 0.0907. 9.07 x 10 – 2. 0.000506.

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How big?

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  1. How big? How small? Significant Digits 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. How can you tell which digits are significant All non zero numbers are significant All zeros that are located between two non zero numbers are significant Zeros that are located to the left of a value are not significant Zeros that are located to the right of a value may or may not be significant.

  5. How many significant digits in each? 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 • The value with the fewest number of decimal places, going into the calculation determines the number of decimal that you should report in your answer.

  8. Adding with Significant Digits • 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

  9. i) ii) iii) 83.25 4.02 0.2983 – 0.1075 + 0.001 + 1.52 Do the following 83.14 4.02 1.82

  10. Multiplication and Division • The value with the fewest number of significant digits, going into the calculation determines the number of significant digits that you should report in your answer. • 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 • recall: for long questions, don’t round until the end)

  11. iv) 6.12 x 3.734 + 16.1  2.3 22.85208 + 7.0 i) 7.255  81.334 = Answers 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) = 29.9

  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

  13. Convert the following 1) 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 Page 77 – 79 Do the worksheet posted on the class site Posted under homework, Unit 1- Matter and Bonding, significant figures worksheet

  14. Solving simple math • Solve each question for x • x = 3 + 4 * 8 • 3x = 18__ • 3 • c. 5 = 2 • x • d. 6 = 2x • 4 • e. 16 = x – 5 • 10 • f. 26 = 3(4) + (x) 22 • 2 35 2 2/5 = 0.4 12 165 7 Page 77 – 79

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