Perform the operations and simplify. a) (2 103)(4 102) b) 3 103 4 105 Solution a) (2 103)(4 102) (2 4)(103 102) 8 105 800,000 3 103 4 105 b) 3 4 103 105 0.75 102 Write 3 4 Commutative property Add the exponents. in decimal form. 7.5 103 Use scientifi c notation. or 0.0075 YOU TRY 4 Perform the operations, and simplify. a) (2.6 102)(5 104) b) 7.2 109 6 105 ANSWERS TO YOU TRY EXERCISES 1) a) 0.83 b) 0.045 c) 1070 2) a) 30,500 b) 0.000083 c) 6918.53 3) a) 1.45824 1013 dollars b) 1.0 103 in. 4) a) 13,000,000 b) 0.00012 EXAMPLE 4 In-Class Example 4 Perform the operations and simplify. a) (3 106)(8 103) b) 5 104 2 109 Answer: a) 24,000,000,000 or 2.4 1010 b) 0.000025 or 2.5 105 10.3 Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. Objectives 1: Understand Scientific Notation Determine whether each number is in scientifi c notation. 1) 7.23 105 yes 2) 24.0 103 no 3) 0.16 104 no 4) 2.8 104 yes 5) 37 102 no 6) 0.9 101 no 7) 5 106 yes 8) 7.5 210 no 9) Explain, in your own words, how to determine whether a number is expressed in scientifi c notation. Answers may vary. 10) Explain, in your own words, how to write 4.1 103 without an exponent. Answers may vary. 11) Explain in your own words, how to write 7.26 104 without an exponent. Answers may vary. Multiply. 12) 980.2 104 13) 0.1502 108 15,020,000 9,802,000 14) 71.765 102 7176.5 15) 40.6 103 0.0406 16) 0.0674 101 0.00674 17) 1,200,006 107 0.1200006 Write each number without an exponent. 18) 1.92 106 1,920,000 19) 6.8 105 0.000068 20) 2.03449 103 21) 5.26 104 52,600 2034.49 22) 7 104 0.0007 23) 8 106 0.000008 24) 9.5 103 0.0095 25) 6.021967 105 602,196.7 26) 6 104 60,000 27) 3 106 3,000,000 28) 9.815 102 0.09815 29) 7.44 104 0.000744 30) 4.1 106 0.0000041 Write the following quantities without an exponent. 31) About 2.4428 107 Americans played golf at least 2 times in a year. (www.census.gov) 24,428,000 32) In 2011, Facebook claimed that over 2.5 108 photos were uploaded each day. (www.facebook.com) 250,000,000 photos 33) The radius of one hydrogen atom is about 2.5 1011 m. 0.000000000025 m 34) The length of a household ant is 2.54 103 m. 0.00254 m 788 CHAPTER 10 The Rules of Exponents and Polynomials www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
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