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Scientific Notation

Scientific Notation. Math 7. Scientific Notation.

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Scientific Notation

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  1. Scientific Notation Math 7

  2. Scientific Notation Numbers are usually written in standard form. For example, 17,900,000 is in standard form. Scientific notation is a kind of shorthand that can be used to write large numbers. Numbers expressed in scientific notation are written as the product of two factors. In scientific notation, 17,900,000 is written as 7 1.79 x 10 A power of 10 A number greater than or equal to 1 but less than 10

  3. Scientific Notation Writing Math In scientific notation, it is customary to use a multiplication cross () instead of a dot.

  4. 6 places Scientific Notation Example 1: Writing Numbers in Scientific Notation Write the number in scientific notation. A. 4,340,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. 4,340,000 = 4,340,000 The exponent is equal to the number of places the decimal point is moved. = 4.34  106

  5. 8 places Scientific Notation Example 2: Writing Numbers in Scientific Notation Write the number in scientific notation. B. 327,000,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. 327,000,000 = 327,000,000 The exponent is equal to the number of places the decimal point is moved. = 3.27  108

  6. 6 places Scientific Notation Try This: Example 3 Write the number in scientific notation. A. 8,421,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. 8,421,000 = 8,421,000 The exponent is equal to the number of places the decimal point is moved. = 8.421  106

  7. 5 places Scientific Notation Try This: Example 4 Write the number in scientific notation. B. 327,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. 327,000 = 327,000 The exponent is equal to the number of places the decimal point is moved. = 3.27  105

  8. Scientific Notation Example 5: Writing Numbers in Standard Form The population of China in the year 2000 was estimated to be about 1.262  109. Write this number in standard form. Since the exponent is 9, move the decimal point 9 places to the right. 1.262 109 = 1.262000000 = 1,262,000,000 The population of China was about 1,262,000,000 people.

  9. Scientific Notation Try This: Example 6 The distance from the Earth to the Sun is calculated to be 1.5  108 kilometers. Write this distance in standard form. Since the exponent is 8, move the decimal point 8 places to the right. 1.5 108 = 1.50000000 = 150,000,000 The distance from the Earth to the Sun is about 150,000,000 kilometers.

  10. Scientific Notation Additional Practice Problems Write each number in scientific notation. 1.5,209 2.830,000,000 3. 42,000,000 4. 2,001,600 5. 652,000 5.209 x 103 8.3 x 108 4.2 x 107 2.0016 x 106 6.52 x 105

  11. Scientific Notation Additional Practice Problems Write each number in standard notation. 1.2.4 x 108 2.9.05 x 106 3. 5.284 x 105 4. 1.17 x 107 5. Earth is about 9.292  107 miles from the Sun. Write this number in standard form. 240,000,000 9,050,000 528,400 11,700,000 92,920,000

  12. Time for Brainpop! http://www.brainpop.com/math/numbersandoperations/standardandscientificnotation/

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