We learned, also, that multiplying a number by 0.1, 0.01, etc. moves the decimal point to the left. This is the same as multiplying a number by a negative power of 10. EXAMPLE 1 In-Class Example 1 Multiply. a) 495 107 b) 6.3 101 Answer: a) 0.0000495 b) 0.63 Multiply. a) 367 104 b) 5.9 101 Solution a) 367 104 367 1 10,000 367 0.0001 0.0367 b) 5.9 101 5.9 1 10 5.9 0.1 0.59 When we multiply each of these numbers by a negative power of 10, the result is smaller than the original number. The exponent determines how many places to the left the decimal point is moved: 367 104 0367. 104 0.0367 4 places to the left 5.9 101 5.9 101 0.59 1 place to the left YOU TRY 1 Multiply. a) 83 102 b) 45 103 c) 10.7 102 It is important to understand the previous concepts to understand how to use scientifi c notation. Definition A number is in scientifi c notation if it is written in the form a 10n, where 1 |a| 10 and n is an integer. That is, |a| is greater than or equal to 1 and less than 10. Note If a is positive, then multiplying a by a positive power of 10 will result in a number that is larger than a. Multiplying a by a negative power of 10 will result in a number that is smaller than a. In your notes, explain how to determine whether a number is in scientific notation. Include examples. In other words, a number in scientifi c notation has one nonzero digit to the left of the decimal point and the number is multiplied by a power of 10. Here are some examples of numbers written in scientifi c notation: 3.82 105, 1.2 103, and 7 102 www.mhhe.com/messersmith SECTION 10.3 Scientific Notation 785
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