EXAMPLE 3 In-Class Example 3 Write each number in scientific notation. a) In 2010, New York City’s population was approximately 8,200,000 people. b) The speed of a garden snail is 0.03 mph. Answer: a) 8.2 106 people b) 3 102 mph Write each number in scientifi c notation. Solution a) The distance from Earth to the sun is approximately 150,000,000 km. 150,000,000. 150,000,000. Move decimal point 8 places. a Decimal point Decimal point will be here. is here. 150,000,000 km 1.5 108 km b) A single rhinovirus measures 0.00002 mm across. 0.00002 mm 0.00002 mm 2 105 mm Decimal point will be here. Procedure Writing a Number in Scientific Notation 1) Locate the decimal point in the original number. 2) Determine where the decimal point will be when converting to scientifi c notation. Remember, there will be one nonzero digit to the left of the decimal point. 3) Count how many places you must move the decimal point to take it from its original place to its position for scientifi c notation. 4) If the absolute value of the resulting number is smaller than the absolute value of the original number, you will multiply the result by a positive power of 10. Example: 350.9 3.509 102 If the absolute value of the resulting number is larger than the absolute value of the original number, you will multiply the result by a negative power of 10. Example: 0.0000068 6.8 106 YOU TRY 3 Write each number in scientifi c notation. a) The gross domestic product of the United States in 2010 was approximately $14,582,400,000,000. (www.worldbank.org) b) The diameter of a human hair is approximately 0.001 in. 3 Perform Operations with Numbers in Scientific Notation We use the rules of exponents to perform operations with numbers in scientifi c notation. www.mhhe.com/messersmith SECTION 10.3 Scientific Notation 787
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