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Uncertainty

Uncertainty. All about uncertainty _____________________________________. Uncertainty. All about uncertainty ALL measurements have some uncertainty. Uncertainty. _____________ numbers: Examples: ___________________ ___________________ ___________________ ___________________

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Uncertainty

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  1. Uncertainty • All about uncertainty • _____________________________________

  2. Uncertainty • All about uncertainty • ALL measurements have some uncertainty

  3. Uncertainty • _____________ numbers: • Examples: • ___________________ • ___________________ • ___________________ • ___________________ • Have __________________________ because these numbers are __________ • Will never affect “significant figures”

  4. Uncertainty • __________________ numbers: • Examples • _____________________ • _____________________ • Have _____________________________ • Will never affect “significant figures”

  5. Uncertainty • ________________ number • Examples • ___________________________________ • ___________________________________ • ___________________________________ • ___________ have some uncertainty to them • Will always affect “significant figures”

  6. Uncertainty and Measurements • ____________________________________ • ____________________________________ • ____________________________________ I KNOW it is between _________ and __________ graduations (marks): measurement: uncertainty:

  7. Uncertainty and Measurements • Determine graduations and uncertainty • State the digits you can be sure of! • Guess the next digit! (and only the next digit) I KNOW it is between _______ and ________ graduations (marks): measurement: uncertainty:

  8. Uncertainty and Measurements • State the digits you can be sure of! • Guess the next digit! (and only the next digit)

  9. Uncertainty and Measurements _____________________________________________________________________________________________________________________________________________ If your instrument has an uncertainty of ± _______, your measurement will end with _______________________ ________________________________________________ If your instrument has an uncertainty of ± _______, your measurement will end with _______________________ ________________________________________________ If your instrument has an uncertainty of ± _______, your measurement will end with _______________________ ________________________________________________

  10. Uncertainty and Measurements Which of the following would be correct if measured on the ruler below? a) 1.0 cm b) 1.50 cm c) 1.55 cm d) 1.6 cm e) 2.00 cm

  11. Uncertainty and Measurements Which of the following would be correct if measured on the ruler below? (This ruler has an uncertainty of ± 0.02 cm) a) 0.5 cm b) 0.50 cm c) 0.055 cm d) 0.75 cm e) 0.100 cm

  12. Uncertainty and Measurements For the graduated cylinder to the right, provide the following information (Uncertainty is ± ______ mL for this one) What are the graduations? What is the volume?

  13. Scientific Notation – Numbers > 1 Place a decimal so that there is a single digit to the left 18900000 Start counting from the right until you get to the decimal This becomes the exponent for “times 10 to the” Remove digits from the right until proper # of sig. figs.

  14. 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 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.

  15. Did you get it? • 512384000 4 s.f. • 0.0006000 2 s.f. • 0.00251634 5 s.f. • 3540000000 5 s.f.

  16. Significant Figures • Significant figures tell you about the ________________________in a measurement. • Significant figures include all ________________ _______________________________________ 11.84 cm

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

  18. How many Sig. Figs.? Two rules: • #1) If there IS a decimal point in the number: • __________________________________________ __________________________________________

  19. How many Sig. Figs.? 2 3 . 0 0 2 8 0 1 0 0 . 0 6 8 0 0 1 0 0 . 0 0 0

  20. 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 • __________________________________________ __________________________________________

  21. How many Sig. Figs.? 7 4 2 9 3 2 3 0 8 0 0 1 0 0 0 0 0

  22. Significant Practice 320000 8900. 0.0061000 0.1528 60020300 12.00500 0.0005 0.10046

  23. 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.

  24. 0.00259428 (3 s.f.) 54.3675701 (5 s.f.) 8265391000 (2 s.f.) 0.1659822 (4 s.f.) 0.0005473300 (5 s.f.) 2617890100 (6 s.f.)

  25. Calculations with Sig. Figs. • Multiplication and division • _______________________________________ _______________________________________ _______________________________________ 1.5 x 7.3254 = 1 0 .9881 6.127 x 0.0000267030 = 0.000163 6 09

  26. Calculations with Sig. Figs. 927.381 / 456.0 0.00159 / 2

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

  28. 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: • _________________________________________ _________________________________________ _________________________________________

  29. Precision 347000 0.000254 10050. 637300000000 0.0790000 0.02

  30. Adding and subtracting with sig. figs. 394.0150 + 0.0074121

  31. Adding and subtracting with sig. figs. 0.0025647 + 0.000321

  32. Adding and subtracting with sig. figs. 682300 + 5922.60 1110000 – 69100

  33. 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 Some More Practice

  34. Mixed Operations with sig. figs. 1) ________________________________________________ 2) ________________________________________________ 3) ________________________________________________ 4) ________________________________________________

  35. Mixed Operations with sig. figs.

  36. Mixed Operations with sig. figs.

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