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Numerical Value

Numerical Value. Scientific Notation and Significant Figures (aka sig figs). Scientific Notation (sci not). Are a set of rules, using the power of ten to ‘shorten’ the number. Numerical Short Cut. What happens when you move the decimal left?. Makes the number SMALLER

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Numerical Value

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  1. Numerical Value Scientific Notation and Significant Figures (aka sig figs) Significant Figures and Scientific Notation

  2. Scientific Notation (sci not) Are a set of rules, using the power of ten to ‘shorten’ the number. Numerical Short Cut Significant Figures and Scientific Notation

  3. What happens when you move the decimal left? Makes the number SMALLER Numbers have positive exponents Exponent value = number of times you move the decimal Moving the Decimal Left Significant Figures and Scientific Notation

  4. Practice – Scientific Notation Write in scientific notation • 1, 000 • 1.0 x 103 • 258, 000 • 2.58 x 105 Significant Figures and Scientific Notation

  5. Practice – Sci Not (Individual) Write in scientific notation • 2, 567, 000 • 340 • 56, 000, 000, 000, 000 • 6 Significant Figures and Scientific Notation

  6. What happens when you move the decimal right? Makes the number BIGGER Numbers have negative exponents Exponent value = number of times you move the decimal Moving the Decimal Right Significant Figures and Scientific Notation

  7. Practice – Scientific Notation Write in scientific notation • 0.015 • 1.5 x 10-2 • 0.0 000 258 • 2.58 x 10-5 Significant Figures and Scientific Notation

  8. Practice – Sci Not (Individual) Write in scientific notation • 0.000 000 002 567 • 0.340 • 0.000 000 000 000 0560 • 0.00 006 Significant Figures and Scientific Notation

  9. Homework: Scientific Notation • Chapter 2, Section 2 (2.2); Page 41 • Problem 11 (complete one a-d) • Problem 11 (complete one e-h) • Problem 12 (complete a and b) Significant Figures and Scientific Notation

  10. Significant Figures (numbers) Are sets of rules that show the best value for a number. Significant Figures Significant Figures and Scientific Notation

  11. Nonzero Numbers • Nonzero numbers are any number whose value is not zero. • Here are some examples of nonzero numbers: • 1 • 22 • 1, 789, 958 Significant Figures and Scientific Notation

  12. Nonzero Numbers - Rules • Count ALL nonzero numbers. • How many nonzero numbers are in each problem? • 12 • Two – so two sig figs • 1135 • Four – so four sig figs Significant Figures and Scientific Notation

  13. Practice – Nonzero # (Solo) • How many significant figures are in the numbers below? • 132, 456 • 7, 896 • 9 Significant Figures and Scientific Notation

  14. Practice – Nonzero # (Solo) Answers • How many significant figures are in the numbers below? • 132, 456 = 6 sig fig • 7, 896 = 4 sig fig • 9 = 1 sig fig Significant Figures and Scientific Notation

  15. Zeros – between numbers Zeros between two nonzero numbers are significant. Count all zeros between numbers. Zeros Between Numbers Significant Figures and Scientific Notation

  16. Practice – Zeros b/w Numbers • How many significant figures are in each example? • 1001 - • 10.005 - • 805 - Significant Figures and Scientific Notation

  17. Practice – Zeros b/w Numbers Answers • How many significant figures are in each example? • 1001 – 4 sig fig • 10.005 – 5 sig fig • 805 – 3 sig fig Significant Figures and Scientific Notation

  18. Zeros to right All zeros to the right (>) of a number are NOT significant unless there is a DECIMAL point. Whole Number Zeros Significant Figures and Scientific Notation

  19. How many sig figs? 10 – 1 sig fig 10 Practice – Zeros to Right Significant Figures and Scientific Notation

  20. How many sig figs? 15000 – 2 sig figs 15000 Practice – Zeros to Right Significant Figures and Scientific Notation

  21. How many sig figs? 150. – 3 sig figs Significant Figures 150. Significant Figures and Scientific Notation

  22. Practice – Zeros to right • How many significant figures are in each example? • 100 - • 10.00 - • 800, 000 - Significant Figures and Scientific Notation

  23. Zeros – WITH the decimals All zeros to the left ()of the first nonzero number are not significant. Zeros with Decimals Significant Figures and Scientific Notation

  24. How many sig figs? 0.000 000 15 0.00000015 2 sig figs Practice – Zeros with Decimals Significant Figures and Scientific Notation

  25. How many sig figs? 0.01 0.01 1 sig figs Practice – Zeros with Decimals Significant Figures and Scientific Notation

  26. Zeros – WITH the decimals Zeros to the right () of the last nonzero number are significant Zeros with Decimals Significant Figures and Scientific Notation

  27. How many sig figs? 0.150 000 00 0.150 000 00 8 sig figs Practice – Zeros with Decimals Significant Figures and Scientific Notation

  28. How many sig figs? 0.0000010 0.0000010 2 sig figs Practice – Zeros with Decimals Significant Figures and Scientific Notation

  29. How many sig figs? 0.015 – 0.1500 – 0.0010100 – Practice – Zeros (individual) Significant Figures and Scientific Notation

  30. How many sig figs? Answers 0.015 – 2 sig figs 0.1500 – 4 sig figs 0.0010100 – 5 sig figs Practice – Zeros (individual) Significant Figures and Scientific Notation

  31. https://www.youtube.com/watch?v=puvE8hF6zrY Video – sig figs (a way to practice) Significant Figures and Scientific Notation

  32. You try it! 360000 5060 360.0100 0.00485 1.00 x 1010 Practice – All the Rules Significant Figures and Scientific Notation

  33. Homework: Scientific Notation • Chapter 2, Section 3 (2.3); Page 51 • Problem 35 (a and b) • Problem 36 (a and b) • Problem 37 Significant Figures and Scientific Notation

  34. Calculations: Add/Subtract Do all the math first. The final answer’s sig figs will depend on the number with the least number of decimals. Calcuations: Add/Subtract Significant Figures and Scientific Notation

  35. Report Answer in Correct Sig Figs 1.0+2.12+0.65 = 15.595+2.4456-2.9 = Practice – Add/Subtract Significant Figures and Scientific Notation

  36. Report Answer in Correct Sig Figs 1.0+2.12+0.65 = 3.77 (1 decimal place) 3.8 Practice – Add/Subtract Significant Figures and Scientific Notation

  37. Report Answer in Correct Sig Figs 15.595+2.4456-2.9 = 15.1406 (1 dec. place) 15.1 Practice – Add/Subtract Significant Figures and Scientific Notation

  38. Report Answer in Correct Sig Figs 16+1.7 12.037-3.93 0.073 +10.0037 3.78 x 104 -2.3 x 103 Practice – Add/Subtract (solo) Significant Figures and Scientific Notation

  39. Report Answer in Correct Sig Figs 16+1.7 = 17.7 = 18 12.037-3.93 = 8.107000000000001 = 8.11 0.073 +10.0037 = 10.0767 = 10.077 3.78 x 104 -2.3 x 103 = 35500 = 3.55 x 104 Practice – Add/Subtract (solo) Significant Figures and Scientific Notation

  40. Calculations: Multiplication/Division Do all the math first. The final answer’s sig figs will depend on the number with the least number of sig figs. Calculation: Mult/Div Significant Figures and Scientific Notation

  41. Practice – Mult/Div (Group) Report answer in the correct number of significant figures. • 10x2.75/0.500 = • (2.00 x 102)(0.2056) = Significant Figures and Scientific Notation

  42. Practice – Mult/Div (Group) Report answer in the correct number of significant figures. • 10x2.75/0.500 = 55 = 60 • (2.00 x 102)(0.2056) = 41.12 = 41.1 Significant Figures and Scientific Notation

  43. Practice – Mult/Div (Indiv) Report answer in the correct number of significant figures. • (5.5)3 = • 45 × 3.00 = • 45 × 3 = Significant Figures and Scientific Notation

  44. Practice – Mult/Div (Indiv) Report answer in the correct number of significant figures. • (5.5)3 = 166.375 = 170 • 45 × 3.00 = 135 = 140 • 45 × 3 = 135 = 100 Significant Figures and Scientific Notation

  45. 4 222 8700 30.4020 2005x18.36x2.3 20.4x0.5 2.2+80.801+71 2.4+0.05+0.00123456 222-2.006X102/10.0 750x0.34+2.62/20 All: Answer in Correct Sig Fig Significant Figures and Scientific Notation

  46. You try it! Tell which rule to use and number of sig figs. For math, report answer in correct sig. figs. 1 sig fig 3 sig fig 2 sig fig 6 sig fig 84667.14 = 84000 or 8.4x104 10.2 = 10 or 1 x 101 154.001 = 154 2.45123456 = 2.5 22.202006 =22.2 745.5882353 = 700 or 7 x 101 All: Answer in Correct Sig Fig Significant Figures and Scientific Notation

  47. Alternatives Considered Homework: • problems 2:12 (a, b, e, f) • problems 2:13 (a-d) • problems 2:14 (e, f, g, h) • problems 2:15 (a-d) • problems 2:16 (a-d) • Or worksheet! Significant Figures and Scientific Notation

  48. Websites for help • Uncertainty in Measurements - http://antoine.frostburg.edu/cgi-bin/senese/tutorials/sigfig/index.cgi • Significant Figures - http://science.widener.edu/svb/tutorial/sigfigurescsn7.html • Applet: Significant Figures - http://www.lon-capa.org/~mmp/applist/sigfig/sig.htm • Significant Figures Games - http://www.mangahigh.com/en_us/maths_games/number/rounding_accuracy_and_estimation/round_using_significant_figures • Significant Figures Explanation - https://www.youtube.com/watch?v=puvE8hF6zrY • Adding and Subtractinghttp://sigfigscalculator.appspot.com/tutorial/add_and_subtract Significant Figures and Scientific Notation

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