The following numbers are not in scientifi c notation: 51.94 104 0.61 103 300 106 c c c 2 digits to left Zero is to left 3 digits to left of decimal point of decimal point of decimal point Now let’s convert a number written in scientifi c notation to a number without exponents. EXAMPLE 2 In-Class Example 2 Rewrite without exponents. a) 1.745 103 b) 1.07 102 c) 3.904 104 Answer: a) 1745 b) 0.0107 c) 39,040 Rewrite without exponents. a) 5.923 104 b) 7.4 103 c) 1.8875 103 Solution a) 5.923 104 S5.9230 59,230 Remember, multiplying by a positive power of 4 places to the right 10 will make the result larger than 5.923. b) 7.4 103 S007.4 0.0074 Multiplying by a negative power of 10 will 3 places to the left make the result smaller than 7.4. c) 1.8875 103 S1.8875 1887.5 3 places to the right How does this process compare to Example 1? YOU TRY 2 Rewrite without exponents. a) 3.05 104 b) 8.3 105 c) 6.91853 103 2 Write a Number in Scientific Notation Let’s write the number 48,000 in scientifi c notation. To write the number 48,000 in scientifi c notation, fi rst locate its decimal point: 48,000. Next, determine where the decimal point will be when the number is in scientifi c notation: 48,000. Decimal point will be here. Therefore, 48,000 4.8 10n, where n is an integer. Will n be positive or negative? We can see that 4.8 must be multiplied by a positive power of 10 to make it larger, 48,000. 48000. a Decimal point Decimal point will be here. starts here. Now we count four places between the original and the fi nal decimal place locations. 48000. 1 2 3 4 We use the number of spaces, 4, as the exponent of 10. 48,000 4.8 104 786 CHAPTER 10 The Rules of Exponents and Polynomials www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
To see the actual publication please follow the link above