Mat 092 section 12.3 scientific notation

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1. Slide - 1Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G 2 Exponents and Polynomials 12 2. Slide - 2Copyright © 2018, 2014, 2010…
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  • 1. Slide - 1Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G 2 Exponents and Polynomials 12
  • 2. Slide - 2Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G 1. Express numbers in scientific notation. 2. Convert numbers in scientific notation to numbers without exponents. 3. Use scientific notation in calculations. Objectives 12.3 An Application of Exponents: Scientific Notation
  • 3. Slide - 3Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Express Numbers in Scientific Notation Numbers occurring in science are often extremely large or extremely small. Because of the difficulty of working with many zeros, scientists often express such numbers with exponents, using a form called scientific notation. In scientific notation, there is always one nonzero digit before the decimal point.
  • 4. Slide - 4Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Express Numbers in Scientific Notation Writing a Number in Scientific Notation A number is written in scientific notation when it is expressed in the form where and n is an integer. 10 ,n a 1 10a 
  • 5. Slide - 5Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Writing a Number in Scientific Notation Step 1 Position the decimal point. Place a caret ^ to the right of the first nonzero digit, where the decimal point will be placed. Step 2 Determine the numeral for the exponent. Count the number of digits from the decimal point to the caret. This number gives the absolute value of the exponent on 10. Step 3 Determine the sign for the exponent. Decide whether multiplying by 10n should make the result of Step 1 greater or less. • The exponent should be positive to make the result greater. • The exponent should be negative to make the result less. Express Numbers in Scientific Notation
  • 6. Slide - 6Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G (a) 153,000,000,000 Example Write each number in scientific notation. Express Numbers in Scientific Notation Reading from left to right, the first nonzero digit is 1. So, we will put the decimal point to the right of 1. Since the (invisible) decimal point was to the right of the last zero, we will have to move it to the left 11 places. And, since we moved it to the left, the 11 will be positive. Thus, 153,000,000,000 = 1.53 1011
  • 7. Slide - 7Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G (b) 9547.3 Example (cont) Write each number in scientific notation. Express Numbers in Scientific Notation Reading from left to right, the first nonzero digit is 9. So, we will put the decimal point to the right of 9. Since the decimal point was to the right of 7, we will have to move it to the left 3 places. And, since we moved it to the left, the 3 will be positive. Thus, 9547.3 = 9.5473 103
  • 8. Slide - 8Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G (c) 0.00000005842 Example (cont) Write each number in scientific notation. Express Numbers in Scientific Notation Reading from left to right, the first nonzero digit is 5. So, we will put the decimal point to the right of 5. Since the decimal point was to the right of the first 0, we will have to move it to the right 8 places. And, since we moved it to the right, the 8 will be negative. Thus, 0.00000005842 = 5.842 10–8
  • 9. Slide - 9Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G (d) 6.1134 Example (cont) Write each number in scientific notation. Express Numbers in Scientific Notation Here, the decimal point is already to the right of the first nonzero number, 6. Thus, we do not have to move it, and the exponent of 10 will be 0. 6.1134 = 6.1134 100
  • 10. Slide - 10Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G (a) 4.125 105 Example Write each number without exponents. Convert Numbers in Scientific Notation Since the exponent of 10 is positive 5, we will move the decimal to the right (undoing the scientific notation) 5 places, making our final answer bigger than 4. 4.125 105 = 412,500 (b) 1.456 10–4 Since the exponent of 10 is negative 4, we will move the decimal to the left 4 places, making our final answer smaller than 1. 1.456 10–4 = 0.0001456    
  • 11. Slide - 11Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G (a) (8 106)(3 10–4) Example Perform each calculation. Write answers in scientific notation and also without exponents. Use Scientific Notation in Calculations = 2400 = (8 3)(106 10–4) = (24)(102) 5 7 9 10 (b) 3 10   5 7 9 10 3 10   2 3 10   0.03
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