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The Math of Scientific Notation

The Math of Scientific Notation. Integrated Science Dr. May. Multiplying. 40,000,000,000 x 200,000 = (4.0 x 10 10 ) (2.0 x 10 5 ) 8,000,000,000,000,000 8.0 x 10 15. Multiplying. (4.0 x 10 10 ) (2.0 x 10 5 ) 4.0 x 2.0 = 8.0 10 10 x 10 5 = 10 10 + 5 = 10 15

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The Math of Scientific Notation

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  1. The Math ofScientific Notation Integrated Science Dr. May

  2. Multiplying 40,000,000,000 x 200,000 = (4.0 x 1010) (2.0 x 105) 8,000,000,000,000,000 8.0 x 1015

  3. Multiplying (4.0 x 1010) (2.0 x 105) • 4.0 x 2.0 = 8.0 • 1010 x 105 = 1010 +5 = 1015 (4.0 x 1010) (2.0 x 105) = 8.0 x 1015

  4. Multiplying 40,000,000,000 x 0.000020 = (4.0 x 1010) (2.0 x 10 –5) 800,000 = 8.0 x 105

  5. Multiplying (4.0 x 1010) (2.0 x 10 –5) • 4.0 x 2.0 = 8.0 • 1010 x 10 –5 = 1010 +(–5) = 1010– 5 = 10 5 (4.0 x 1010) (2.0 x 10 –5) = 8.0 x 105

  6. Multiplying 0.00000000040 x 0.000020 = (4.0 x 10 –10) (2.0 x 10 –5) 0.0000000000000080 = 8.0 x 10 –15

  7. Multiplying (4.0 x 10 –10) (2.0 x 10 –5) • 4.0 x 2.0 = 8.0 • 10–10 x 10–5 = 10–10+(–5) = 10–10 –5 = 10–15 (4.0 x 10 –10) (2.0 x 10 –5) = 8.0 x 10 –15

  8. Dividing 4.0 x 1010 2.0 x 105 • 4.0  2.0 = 2.0 • 1010  105 = 1010 – 5 = 105 4.0 x 1010= 2.0 x 105 2.0 x 105

  9. Dividing 4.0 x 1010 2.0 x 10 –5 • 4.0  2.0 = 2.0 • 1010  10 –5 = 1010 – (– 5) = 10 10+5 = 1015 4.0 x 1010= 2.0 x 1015 2.0 x 10 –5

  10. Dividing 4.0 x 10 –10 2.0 x 10 –5 • 4.0  2.0 = 2.0 • 10–10  10–5 = 10–10 – (– 5) = 10–10 + 5 10 –5 4.0 x 10 –10= 2.0 x 10 –5 2.0 x 10 –5

  11. Squaring • (3.0 x 108)2 • (3.0)2 = 9.0 • (108)2 = 102x8 = 1016 (3.0 x 108)2 = 9.0 x 1016

  12. Square Roots ____________ •  9.0 x 1016 _____ _______ •  9.0 = 3.0  1016 = 10 16 2 = 108 _____________  9.0 x 1016 = 3.0 x 10 8

  13. The End • This presentation was created for the benefit of our students by the Science Department at Howard High School of Technology • Please send suggestions and comments to rmay@nccvt.k12.de.us

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