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Scientific Notation

Scientific Notation. Tuesday, February 25 th. Pause for a chat. What should we do when life is frustrating and/or annoying? . Multiplication with Scientific Notation. To multiply numbers in scientific notation: Use your exponent rules!

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Scientific Notation

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  1. Scientific Notation Tuesday, February 25th

  2. Pause for a chat • What should we do when life is frustrating and/or annoying?

  3. Multiplication with Scientific Notation To multiply numbers in scientific notation: Use your exponent rules! (4.0 x 103)(2.0 x 106) = (4.0)(2.0) x (103)(106) = 8.0 x 109

  4. Practice: Scientific Notation What is (3.0 x 105)(2.0 x 106) • 5.0 x 1011 • 5.0 x 1030 • 6.0 x 1011 • 6.0 x 1030

  5. Practice: Scientific Notation What is (3.0 x 105)(2.0 x 106) • 5.0 x 1011 • 5.0 x 1030 • 6.0 x 1011 • 6.0 x 1030

  6. Practice: Scientific Notation What is (3.0 x 102)(4.0 x 105) • 1.2 x 107 • 1.2 x 108 • 1.2 x 1010 • 7.0 x 1010

  7. Practice: Scientific Notation What is (3.0 x 102)(4.0 x 105) • 1.2 x 107 • 1.2 x 108 • 1.2 x 1010 • 7.0 x 1010

  8. Scientific Notation Example: (4.0 x 103)(3.0 x 106) = (4.0)(3.0) x (103)(106) = 12.0 x 109 = 1.2 x 101 x 109 = 1.2 x 1010

  9. Practice: Scientific Notation What is (3.0 x 10–2)(3.0 x 105) • 6.0 x 10-10 • 6.0 x 107 • 9.0 x 10-10 • 9.0 x 103

  10. Practice: Scientific Notation What is (3.0 x 10–2)(3.0 x 105) • 6.0 x 10-10 • 6.0 x 107 • 9.0 x 10-10 • 9.0 x 103

  11. Practice: Scientific Notation What is (5.0 x 10–2)(3.0 x 105) • 8.0 x 103 • 8.0 x 104 • 1.5 x 103 • 1.5 x 104

  12. Practice: Scientific Notation What is (5.0 x 10–2)(3.0 x 105) • 8.0 x 103 • 8.0 x 104 • 1.5 x 103 • 1.5 x 104

  13. Division with scientific notation 6.0 x 105 2.0 x 108 = 3.0 x 105 – 8 = 3.0 x 10–3

  14. Practice: Scientific Notation What is (6.0 x 10–2)/(3.0 x 105) • 2.0 x 103 • 2.0 x 107 • 2.0 x 10-3 • 2.0 x 10-7

  15. Practice: Scientific Notation What is (6.0 x 10–2)/(3.0 x 105) • 2.0 x 103 • 2.0 x 107 • 2.0 x 10-3 • 2.0 x 10-7

  16. Practice: Scientific Notation What is (8.0 x 10–4)/(2.0 x 10-9) • 4.0 x 10–13 • 4.0 x 105 • 6.0 x 10–13 • 6.0 x 105

  17. Practice: Scientific Notation What is (8.0 x 10–4)/(2.0 x 10-9) • 4.0 x 10–13 • 4.0 x 105 • 6.0 x 10–13 • 6.0 x 105

  18. Prefixes and Scientific Notation Example: 3.2 kilometers = 3.2 x 103 m Large numbers: Deca – 101 Hecto– 102 Kilo – 103 Mega – 106 Giga – 109 Tera– 1012

  19. Practice: Scientific Notation Convert 56 kilometers into meters. • 5.6 x 103 • 5.6 x 104 • 5.6 x 10-3 • 5.6 x 10-4

  20. Practice: Scientific Notation Convert 56 kilometers into meters. • 5.6 x 103 • 5.6 x 104 • 5.6 x 10-3 • 5.6 x 10-4

  21. Practice: Scientific Notation Convert 1.21 gigawatts into watts. • 1.21 x 106 • 1.21 x 109 • 1.21 x 1011 • 1.21 x 1012 1.21 Jiggawatts

  22. Practice: Scientific Notation Convert 1.21 gigawatts into watts. • 1.21 x 106 • 1.21 x 109 • 1.21 x 1011 • 1.21 x 1012 1.21 Jiggawatts

  23. Practice: Scientific Notation Convert 128 gigabits into bits. • 1.28 x 107 • 1.28 x 109 • 1.28 x 1011 • 1.28 x 1012

  24. Practice: Scientific Notation Convert 128 gigabits into bits. • 1.28 x 107 • 1.28 x 109 • 1.28 x 1011 • 1.28 x 1012

  25. Scientific Notation Simplification Worked example: simplify (3.0 x 109)(0.002) (4.0 x 105)

  26. Applications of Scientific Notation Example: How many pixels are in a 2.5 megapixel photo? • 2.5 x 103 • 2.5 x 106 • 2.5 x 109 • 2.5 x 1012

  27. Applications of Scientific Notation Example: How many pixels are in a 2.5 megapixel photo? • 2.5 x 103 • 2.5 x 106 • 2.5 x 109 • 2.5 x 1012

  28. Applications of Scientific Notation Example: It takes 4.0 bytes of space to store a single pixel. How many bytes does it take to store a 2.5 megapixel photo. • 1.0 x 106 • 1.0 x 107 • 1.0 x 108 • 1.0 x 109

  29. Applications of Scientific Notation Example: It takes 4.0 bytes of space to store a single pixel. How many bytes does it take to store a 2.5 megapixel photo. • 1.0 x 106 • 1.0 x 107 • 1.0 x 108 • 1.0 x 109

  30. Applications of Scientific Notation Example: It takes 4.0 bytes of space to store a single pixel in a 2.5 megapixel photo. How many pictures would fit on a 200 gigabyte hard disk? • 2x 104 • 2 x 105 • 2 x 106 • I need a hand with this one. (note: I’m using the regular definition of giga meaning 109, not to be confused with gibibytes meaning 1073741824 bytes)

  31. Applications of Scientific Notation Example: It takes 4.0 bytes of space to store a single pixel in a 2.5 megapixel photo. How many pictures would fit on a 200 gigabyte hard disk? • 2 x 104 • 2 x 105 • 2 x 106 • I need a hand with this one. (note: I’m using the regular definition of giga meaning 109, not to be confused with gibibytes meaning 1073741824 bytes)

  32. Applications of Scientific Notation Example: Sound travels at 3.4 x 102 m/s. There are 3.15 x 107 seconds in a year. How far would sound travel in a year if it didn’t dissipate? • 1.071 x 109 m • 1.071 x 1010 m • 1.071 x 1011 m • 1.071 x 1012 m

  33. Applications of Scientific Notation Example: Sound travels at 3.4 x 102 m/s. There are 3.15 x 107 seconds in a year. How far would sound travel in a year if it didn’t dissipate? • 1.071 x 109 m • 1.071 x 1010 m • 1.071 x 1011 m • 1.071 x 1012 m

  34. Practice in your teams! Mass can convert to energy by the equation, E = mc2, and c is the speed of light (3.0 x 108 m/s). a. How much energy is stored in the mass of your math textbook (approximately 0.5kg)? b. How much mass would you need to provide energy electrical energy to power every grid in the world for one hour? The world uses approximately 8.6 x 1018J of energy per hour.

  35. Note for Khan Academy To get 3.1 x 102, type: 3.1 10^2 Get started! Homework: • Page 103 #15 – 21, 26 – 28

  36. Practice individually Homework: • Page 103 #15 – 21, 26 – 28 • Page 115 #17 – 21, 26

  37. Rational Numbers What is a rational number? Any number that can be written as a

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