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What is Scientific Notation?

What is Scientific Notation?. Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise. For very large and very small numbers, scientific notation is more concise.

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What is Scientific Notation?

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  1. What is Scientific Notation? • Scientific notation is a way of expressing really big numbers or really small numbers. • It is most often used in “scientific” calculations where the analysis must be very precise. • For very large and very small numbers, scientific notation is more concise.

  2. How Big Can Our Numbers Be in Chemistry??? • MOLES: 1 (one) Mole of any element contains 602000000000000000000000 pieces In a practical example if you had 1 mole of M & M’s you would have 602000000000000000000000 M & M’s

  3. Because . . . . . . • The particles (atoms) that make up an element are so small they will always be in large numbers – • THEREFORE you MUST put numbers in scientific notation to be able to work with them

  4. When using Scientific Notation, there are two kinds of exponents: positive and negative Positive Exponent: 2.35 x 10 8 Negative Exponent: 3.97 x 10 -7

  5. Putting Numbers in Scientific Notation • A number between 1 and 10 • A power of 10 N x 10x

  6. When changing from Standard Notation to Scientific Notation: 1) First, move the decimal after the first whole number: 3 2 5 8 2) Second, add your multiplication sign and your base (10). 3 . 2 5 8 x 10 3) Count how many spaces the decimal moved and this is the exponent. 3 . 2 5 8 x 10 3 3 2 1

  7. When changing from Standard Notation to Scientific Notation: 4) See if the original number is greater than or less than one. • If the number is greater than one, the exponent will be positive. 348943 = 3.489 x 105 • If the number is less than one, the exponent will be negative. .0000000672 = 6.72 x 10-8

  8. More Examples • Given: 289,800,000 • Use: 2.898 (moved 8 places) • Answer:2.898 x 108 • Given: 0.000567 • Use: 5.67 (moved 4 places) • Answer:5.67 x 10-4

  9. To change scientific notation to standard form… • Simply move the decimal point to the right for positive exponent 10. • Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

  10. Example • Given: 5.093 x 106 • Answer: 5,093,000 (moved 6 places to the right) • Given: 1.976 x 10-4 • Answer: 0.0001976 (moved 4 places to the left)

  11. Learning Check • Express these numbers in Scientific Notation: • 405789 • 0.003872 • 3000000000 • 2 • 0.478260

  12. Using numbers in scientific notation in a a calculator to evaluate: 4.5 x 10-5 1.6 x 10-2 Type 4.5 -5 1.6 - 2 You must include parentheses if you don’t use those buttons!! (4.5 x 10 -5) (1.6 x 10 -2) 0.0028125 Write in scientific notation. 2.8125 x 10-3

  13. Use a calculator to evaluate: 7.2 x 10-9 1.2 x 102On the calculator, the answer is: 6.E -11 The answer in scientific notation is 6 x 10 -11 The answer in decimal notation is 0.00000000006

  14. 6) Use a calculator to evaluate (0.0042)(330,000).On the calculator, the answer is 1386. The answer in decimal notation is 1386 The answer in scientific notation is 1.386 x 103

  15. LA RULE • Left Add – if you move the decimal to the left you add to the exponent • If you move the decimal right you -??????

  16. Using Numbers in Scientific notation: • Adding & Subtracting • Rule #1 – the exponents must be the same • Examples: 3.5 x 103 + 2.5 x 103 = 6 x 103 5.8 x 1010 - 4.5 x 1010 = 1.3 x 1010 IF THEY ARE NOT THE SAME . . . . . .

  17. What if they do not have the same exponent? • Rule – If not in scientific notation you must change the exponents • Examples: 3.5 x 105 + 2.5 x 103 = (350 x 103 + 2.5 x 103 = 352.5 x 103) put in correct scientific notation – 3.525 x 105 5.8 x 1010 - 4.5 x 108 = (5.8 x 1010 - .045 x 1010 = 5.755 x 1010)

  18. Using Numbers in Scientific notation: • Multiplying and Dividing Rule– if multiplying, add the exponents if dividing, subtract the exponents Examples: 2.2 x 103 x 1.0 x 103 = 2.2 x 106 4.5 x 104 / 5.6 x 103 = .80357 x 101 (8.0357 x 100)

  19. Learning Check • Multiply or Divide: • (4.05789 x 103) (2.7 x 10-2) • (3.872 x 1010)/(1.55 x 103)

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