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Scientific Notation

Scientific Notation. The Long Way. 4700 = 470 x 10 = 47 x 10 x 10 = 4.7 x 10 x 10 x 10. 4.7 x 10 x 10 x 10 = 4.7 x (10 3 ). Definitions. 4.7 x (10 3 ) is called the standard form of 4700. It is in scientific notation if the number at the start (4.7) lies between 1 and 10.

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Scientific Notation

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  1. Scientific Notation

  2. The Long Way 4700 = 470 x 10 = 47 x 10 x 10 = 4.7 x 10 x 10 x 10 4.7 x 10 x 10 x 10 = 4.7 x (103)

  3. Definitions 4.7 x (103) is called the standard form of 4700. It is in scientific notation if the number at the start (4.7) lies between 1 and 10

  4. Examples Write the following in scientific notation. • 83000 = 8300 x 10 = 830 x 10 x 10 = 83 x 10 x 10 x 10 = 8.3 x 10x 10 x 10 x 10 = 8.3 x (104) 8.3 lies bewteen 1 and 10

  5. Examples Write the following in scientific notation. 2. 631000 = 63100 x 10 = 6310 x 10 x 10 = 631 x 10 x 10 x 10 = 63.1 x 10 x 10 x 10 x 10 = 6.31 x 10 x 10 x 10 x 10 x 10 = 6.31 x (105) 6.31 lies bewteen 1 and 10

  6. The Short Way Let’s look again at the examples • 83000 = 8300 x 10 = 830 x 10 x 10 = 83 x 10 x 10 x 10 = 8.3 x 10x 10 x 10 x 10 = 8.3 x (104) Changing 83000 to 8.3 meant moving the point 4 places

  7. The Short Way Let’s look again at the examples • 631000 = 63100 x 10 = 6310 x 10 x 10 = 631 x 10 x 10 x 10 = 63.1 x 10x 10 x 10 x 10 = 6.31 x 10 x 10 x 10 x 10 x 10 = 6.31 x (105) Changing 631000 to 6.31 meant moving the point 5 places

  8. Examples Write in scientific notation. • 29000 • 3300 • 987000 • 50000 • 701000

  9. Examples Write in scientific notation. • 29000 = 2.9 x 104 • 3300 = 3.3 x 103 • 987000 = 9.87 x 105 • 50000 = 5 x 104 • 701000 = 7.01 x 105

  10. Example Convert from scientific notation to number form • 8.3 x (104) = 8.3 x 10 x 10 x 10 x 10 = 83 x 10 x 10 x 10 = 830 x 10 x 10 = 8300 x 10 = 83000

  11. Example Convert from scientific notation to number form • 6.31 x (105) = 6.31 x 10 x 10 x 10 x 10 x 10 = 63.1 x 10 x 10 x 10 x 10 = 631 x 10 x 10 x 10 = 6310 x 10 x 10 = 63100 x 10 = 631000

  12. The Short Way Let’s look again at the examples 1. 8.3 x (104) = 8.3 x 10 x 10 x 10 x 10 = 83 x 10 x 10 x 10 = 830 x 10 x 10 = 8300 x 10 = 83000 Changing 8.3 to 83000 meant moving the point 4 places to the right

  13. The Short Way 1. 6.31 x (105) = 6.31 x 10 x 10 x 10 x 10 x 10 = 63.1 x 10 x 10 x 10 x 10 = 631 x 10 x 10 x 10 = 6310 x 10 x 10 = 63100 x 10 = 631000 Changing 631000 to 6.31 meant moving the point 5 places to the right

  14. Examples Write in number form. • 7.4 x 103 = • 1.3 x 106 = • 5.51 x 104 = • 3 x 101 = • 4.27 x 107 =

  15. Examples Write in number form. • 7.4 x 103 = 7400 • 1.3 x 106 = 1300000 • 5.51 x 104 = 55100 • 3 x 101 = 30 • 4.27 x 107 = 42700000

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