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Scientific Notation

Scientific Notation. Scientific Notation At the conclusion of our time together, you should be able to:. Define scientific notation Convert numbers into scientific notation Convert scientific notation to a standard number. What is Scientific Notation?.

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Scientific Notation

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  1. Scientific Notation

  2. Scientific NotationAt the conclusion of our time together, you should be able to: Define scientific notation Convert numbers into scientific notation Convert scientific notation to a standard number

  3. What is Scientific Notation? • Scientific notation is a way of expressing really big numbers or really small numbers. • For very large and very small numbers, scientific notation is more concise.

  4. Scientific Notation Consists Of Two Parts: • M = A number between 1 and 10 • n = A power of 10 M x 10n

  5. Scientific Notation M x 10n • M is the coefficient 1<M<10 • 10 is the base • n is the exponent or power of 10

  6. Other Examples: 5.45E+6 5.45 x 10^6

  7. Numbers Less Than 1 Will Have A Negative Exponent. A millionth of a second is: 0.000 001 sec 1 x 10-6 s 1.0E-6 s 1.0 x 10^-6 s

  8. To Change Standard Form To Scientific Notation… • Place the decimal point so that there is one non-zero digit to the left of the decimal point. • Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. • If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

  9. Examples • Given: 289 800 000 m • Use: 2.898 m (moved 8 places) • Answer: 2.898 x 108 m • Easier Way = M term smaller, so make n term larger - 100 to 108 • Given: 0.000 567 m • Use: 5.67 m (moved 4 places) • Answer: 5.67 x 10-4 m • Easier Way = M term larger, so make n term smaller - 100 to 10-4

  10. To Change Scientific Notation To Standard Form… • Simply move the decimal point to the right for positive exponent of 10. • Move the decimal point to the left for negative exponent of 10. (Use zeros to fill in places.)

  11. Example • Given: 5.093 x 106 m • Answer: 5 093 000 m (moved 6 places to the right) • Easier Way = 106 to 100 = n smaller, so make M term larger! • Given: 1.976 x 10-4 m • Answer: 0.000 197 6 m (moved 4 places to the left) • Easier Way = 10-4 to 100 = n larger, so make M term smaller!

  12. Scientific NotationLet’s see if you can: Define scientific notation Convert numbers into scientific notation Convert scientific notation to a standard number

  13. Learning Check • Express these numbers in Scientific Notation: • 405 000 cm • 0.003 872 cm • 3 000 000 000 cm • 2 cm • 0.478000 cm 4.05 x 105 cm 3.872 x 10-3 cm 3 x 109 cm 2 x 100 cm 4.78000 x 10-1 cm

  14. Scientific Notation Calculations

  15. Scientific NotationAt the conclusion of our time together, you should be able to: Multiply and divide numbers that are in scientific notation Add and subtract numbers that are in scientific notation

  16. Example #16 • (3 x 102 m)(8 x 10-4 m) • Answer: multiply M terms • 24 • Add n terms • -2 • 24 x 10-2 m2 • Adjust to correct scientific notation • 2.4 x 10-1 m2 • Adjust to correct number of sig figs • 2 x 10-1 m2

  17. Example #17 • (5.000 x 105 m)/(3500 m) • Answer: divide M terms • 0.001 428 • Subtract n terms • 5 • 0.001 428 x 105 • Adjust to correct scientific notation • 1.428 x 102 • Adjust to correct number of sig figs • 1.4 x 102

  18. Example #18 • (5.0 x 104 m)(8.230 x 106 m) /(1.99 x 1018 m) • Answer: multiply and divide M terms • 20.678 m • Add and subtract n terms • -8 • 20.678 x 10-8 m • Adjust to correct scientific notation • 2.0678 x 10-7 m • Adjust to correct number of sig figs • 2.1 x 10-7 m

  19. Example #13 • (5.0 x 10-3 m)-(5.0 x 10-8 m) • Answer: can only subtract like powers • Adjust to larger power • (5.0 x 10-3 m)-(0.000050 x 10-3 m) = • 4.999950 x 10-3 m • Adjust to correct number of decimal places • 5.0 x 10-3 m • Adjust to correct scientific notation • 5.0 x 10-3 m

  20. Example #14 • (5.0 x 10-3 m) + 0.774 m • Answer: can only add like powers • Adjust to larger power • (0.0050 x 100 m) + 0.774 m = • 0.7790 m • Adjust to correct number of decimal places • 0.779 m • Adjust to correct scientific notation • 7.79 x 10-1 m

  21. Example #15 • (5.0 x 10-3 m) + (5.0 x 10-4 m) - 0.009 38 m • Answer: can only add like powers • Adjust to larger power • (0.0050 x 100 m) + (0.000 50 m) – 0.009 38 m • -0.003 88 m • Adjust to correct number of decimal places • -0.003 9 m • Adjust to correct scientific notation • -3.9 x 10-3 m

  22. Scientific NotationLet’s see if you can: Multiply and divide numbers that are in scientific notation Add and subtract numbers that are in scientific notation

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