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Scientific Notation and Archimedes

This chapter introduces scientific notation and its application in solving problems related to Archimedes and the Golden Crown. Learn how to convert large and small numbers into scientific notation and perform calculations using this notation.

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Scientific Notation and Archimedes

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  1. Chapter 2 Scientific Notation and Archimedes

  2. Scientific Notation

  3. # x 10n • # = greater than or equal to 1 and less than 10. • n = any number …-2,-1,0,1,2…

  4. Scientific Notation .00000775 m 20 700 000 000 000 000 000 m

  5. Scientific Notation 7.75 x 10-6 m 2.07 x 1019m

  6. Scientific Notation 7.75 x 10-6 m 2.07 x 1019m Now multiply them together

  7. (7.75 x 10-6m) x (2.07 x 1019m) = 1.60425 x 1014

  8. (7.75 x 10-6m) x (2.07 x 1019m) = 1.60425 x 1014 1.60 x 1014 m2

  9. Write the number in scientific notation. There are 802 000 000 000 000 000 000 000 copper atoms in this sample of copper sulfate.

  10. 8.02 x 1023 Cu atoms There are 802 000 000 000 000 000 000 000 copper atoms in this sample of copper sulfate.

  11. Write the number in scientific notation. The mass of a proton is 0.000 000 000 000 000 000 000 001 672 67g

  12. 1.67267 x 10-24g The mass of a proton is 0.000 000 000 000 000 000 000 001 672 67g

  13. Practice Problem • 8.02 x 1023 copper atoms

  14. Practice Problem • 8.02 x 1023 copper atoms • Each copper atom contains 29 protons

  15. Practice Problem • 8.02 x 1023 copper atoms • Each copper atom contains 29 protons • Mass of a proton is 1.67267 x 10-24 grams

  16. Practice Problem • 8.02 x 1023 copper atoms. • Each copper atom contains 29 protons • Mass of a proton is 1.67267 x 10-24 grams • What is the mass of all of copper’s protons in the sample?

  17. Practice Problem • 8.02 x 1023 copper atoms. • Each copper atom contains 29 protons • Mass of a proton is 1.67267 x 10-24 grams • What is the mass of all of copper’s protons in the sample? • (8.02 x 1023)(29)(1.67267 x 10-24 g)

  18. Practice Problem • 8.02 x 1023 copper atoms. • Each copper atom contains 29 protons • Mass of a proton is 1.67267 x 10-24 grams • What is the mass of all of copper’s protons in the sample? • (8.02 x 1023)(29)(1.67267 x 10-24 g) = 38.90295886g

  19. Practice Problem • 8.02 x 1023 copper atoms. • Each copper atom contains 29 protons • Mass of a proton is 1.67267 x 10-24 grams • What is the mass of all of copper’s protons in the sample? • (8.02 x 1023)(29)(1.67267 x 10-24 g) = 38.90295886g = 38.9g

  20. Archimedes

  21. Archimedes and the Golden Crown

  22. Homework • Worksheet: Scientific Notation

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