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8.3 Scientific Notation

Learn how to express very large or very small numbers in scientific notation. Practice converting between standard notation and scientific notation.

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8.3 Scientific Notation

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  1. 8.3 Scientific Notation

  2. Scientific Notation 8-3 Scientific Notation

  3. Scientific Notation When dealing with very large or very small numbers, keeping track of place value can be difficult. For this reason, numbers such as these are often expressed in scientific notation. 8-3 Scientific Notation

  4. Scientific Notation Scientific Notation A number is expressed in scientific notation when it is written as a product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than 10. A number in scientific notation is written as a × 10n, where 1 ≤ a < 10 and n is an integer. 8-3 Scientific Notation HANDOUT

  5. Scientific Notation = 4.81 × Examples 6.59 × 104 = 6.59 × 10,000 = 65,900 The decimal point moved 4 places to the right. 8-3 Scientific Notation 4.81 × 10– 6 = 4.81 × 0.000001 = 0.00000481 The decimal point moved 6 places to the left.

  6. Scientific Notation Use these steps to express a number of the forma × 10n in standard notation: • Determine whether n > 0 or n < 0. • If n > 0, move the decimal point in a to the rightn places.If n < 0, move the decimal point in a to the leftn places. • Add zeros, decimal point and/or commas as needed to indicate place value. 8-3 Scientific Notation HANDOUT

  7. Express in standard notation. move decimal point 3 places to the left. Example 3-1a Answer: 0.00748

  8. Express in standard notation. move decimal point 5 places to the right. Example 3-1b Answer: 219,000

  9. Express each number in standard notation. a. b. Example 3-1c Answer: 0.0316 Answer: 7610

  10. Scientific Notation Use these steps to express a number in scientific notation: • Move the decimal point so that it is to the right of the firstnonzero digit.The result is a decimal number a. • Observe the number of places n and the direction in which you moved the decimal point. • If the decimal point moved to the left, write as a × 10n.If the decimal point moved to the right, write as a × 10– n. 8-3 Scientific Notation

  11. Move decimal point 7 places to the right. and Answer: Example 3-2a Express 0.000000672 in scientific notation.

  12. Move decimal point 12 places to the left. and Answer: Example 3-2b Express 3,022,000,000,000 in scientific notation.

  13. Answer: Answer: Example 3-2c Express each number in scientific notation. a. 458,000,000 b. 0.0000452

  14. Scientific Notation You will often see large number in the media written using a combination of a number and a word, such as 3.2 million. To write this number in standard notation, rewrite the word million as 106. The exponent 6 indicates that the decimal point should be moved 6 places to the right. 3.2 million = 3,200,000 8-3 Scientific Notation

  15. Answer: Shoes sold to women: Shoes sold to men: Total spent: Example 3-3a The Sporting Goods Manufacturers Association reported that in 2000, women spent $4.4 billion on 124 million pairs of shoes. Men spent $8.3 billion on 169 million pairs of shoes. Express the numbers of pairs of shoes sold to women, pairs sold to men, and total spent by both men and women in standard notation.

  16. Answer: Shoes sold to women: Shoes sold to men: Total spent: Example 3-3b Write each of these numbers in scientific notation.

  17. Example 3-3c The average circulation for all U.S. daily newspapers in 2000 was 111.5 billion newspapers. The top three leading newspapers were TheWall Street Journal, with a circulation of 1.76 million newspapers, USA Today, which sold 1.69 million newspapers, and TheNew York Times, which had 1.10 million readers. a. Express the average daily circulation and the circulation of the top three newspapers in standard notation. Answer: Total circulation: 111,500,000,000; TheWall Street Journal: 1,760,000; USA Today: 1,690,000; TheNew York Times: 1,100,000

  18. Answer: Total circulation: The Wall Street Journal: USA Today: The New York Times: Example 3-3d The average circulation for all U.S. daily newspapers in 2000 was 111.5 billion newspapers. The top three leading newspapers were TheWall Street Journal, with a circulation of 1.76 million newspapers, USA Today, which sold 1.69 million newspapers, and TheNew York Times, which had 1.10 million readers. b. Write each of the numbers in scientific notation.

  19. Scientific Notation You can use scientific notation to simplify computation with very large and/or very small numbers. 8-3 Scientific Notation

  20. Evaluate Express the result in scientific and standard notation. Product of Powers Answer: Commutative and Associative Properties Product of Powers Associative Property Example 3-4a

  21. Evaluate Express the result in scientific and standard notation. Answer: Example 3-4c

  22. Evaluate Express the result in scientificand standard notation. Associative Property Product of Powers Answer: Example 3-5a

  23. Evaluate Express the result in scientificand standard notation. Answer: Example 3-5b

  24. Practice Problems Page: 428 Problems: 19-55

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