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Scientific Notation

Scientific Notation. Bell Ringers. What is a shorthand way to write 10 x 10 x 10 x 10 using an exponent? 10 4 2. How can you write 0.001 as a power of 10? 10 -3.

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Scientific Notation

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  1. Scientific Notation Bell Ringers What is a shorthand way to write 10 x 10 x 10 x 10 using an exponent? 104 2. How can you write 0.001 as a power of 10? 10-3

  2. Standard: M8N1. Students will understand different representations of numbers including square roots, exponents, and scientific notation.Element: j. Express and use numbers in Scientific NotationEssential Question: How do I translate a number from standard form to Scientific Notation and vice versa?

  3. Scientific notation is the way that scientists easily handle very large numbers or very small numbers. Study these examples looking for a pattern: 235,000 = 2.35 x 105 499,800,000,000 = 4.998 x 1011 307,640,000 = 3.0764 x 108 1,000,000,000,000,000 = 1 x 1015 Do you see a pattern?

  4. Yes, there is a pattern… A number in scientific notation has 2 factors: • The first factor is a number less than 10 and greater than or • equal to 1…in other words IT IS A NON-ZERO 1 DIGIT NUMBER followed by a decimal points and digits. • The second factor is a power of 10…10 with an exponent. The exponent may be positive or negative. More about that soon. Let’s see how it is done!

  5. Let’s write 875,000,000 in scientific notation. 1. Where do you have to put the decimal so that the first factor is less than 10 and greater than or equal to 1? Yes, 8.75 you are to drop any 0’s that are not significant..those that are at the end. 2. Now, how many times would you have to multiply 8.75 by 10 to get 875,000,000? 8 is correct so the exponent is 8. How do we get 8? 875,000,000 in scientific notation is 8.75 x 108

  6. Let’s write 3,047,000 in scientific notation. 1. Where do you have to put the decimal so that the first factor is less than 10 and greater than or equal to 1? Yes, 3.047 you are to drop any 0’s that are not significant..those that are at the end. You must keep the 0 between the 3 and 4. 2. Now, how many times would you have to multiply 3.047 by 10 to get 3,047,000? 6 is correct so the exponent is 6. How do we get 6? 3,047,000 in scientific notation is 3.047 x 106

  7. Try some on your own. Express the following in Scientific Notation: 1. 2,400 = 2.4 x 103 2. 84,000 = 8.4 x 104 3. 5,049,000 = 5.049 x 106 4. 714,000,000,000 = 7.14 x 1011 5. 603,400 = 6.034 x 105

  8. Scientific notation is the way that scientists easily handle very large numbers or very small numbers. Study these examples looking for a pattern: 0.1 = 1 x 10-1 0.023 = 2.3 x 10-2 0.004 = 4 x 10-3 0.0001243 = 1.243 x 10-4 Do you see a pattern?

  9. Try some on your own. Express the following in Scientific Notation: 1. 0.24 = 2.4 x 10-1 2. 0.0084= 8.4 x 10-3 3. 0.5049 = 5.049 x 10-1 4. 0.000000714 = 7.14 x 10-7 6.034 x 10-3 5. 0.006034 =

  10. What is 3.74 x 105 written in standard notation? 374,000 How do we get that? • What is 6.83 x 10-3 written in standard notation? 0.00683 How do we get that? Ready to practice going from scientific notation to standard notation?

  11. Write the following in standard notation: • 2.7 x 103 = • 4.703 x 107 = • 6.82 x 10-4 = • 4. 5 x 10-2 = 2,700 47,030,000 0.000682 0.05

  12. Now, complete your handout! Let’s check the odds: Let’s check the evens: 1. 6 x 10-6 3. 6 x 101 5. 6.7 x 100 7. 2 x 106 9. 4.89 x 104 11. 6.3 x 100 13. 2.16 x 10-4 15. 0.0015 = 1.5 x 10-3 17. 0.09 19. 200,000 21. 26,600 23. 0.775 25. 95,000,000 27. 0.009 29. 0.000075 31. 840,000 • 2. 5.4 x 106 • 4. 9 x 10-3 • 6. 2 x 10-7 • 8. 7.1 x 104 • 10. 9 x 10-7 • 12. 3.3 x 10-2 • 14. 4.2 x 10-3 • 16. 4.8 x 101 • 18. 0.2 • 20. 80,400 • 22. 0.015 • 24. 83,000,000 • 26. 17,100,000 • 28. 3,800 • 30. 4 • 0.00004

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