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1 Chapter 1 Problem Set Key: Scientific Notation and Exponents 1. Give the whole number or fraction that corresponds to these exponential expressions: a. 23 = __8__ b. 31 = _3_ c. 3 –2 = 1/9 d. 3 –3 = 1/27 e. 106 = 1,000,000 f. 10 –7 =0.0000001 g. Explain how to solve 1d using your calculator: Press (3); press (yx), press (3), press (+/-), press (=) h. Explain how to solve 1d without using your calculator: 1/3 x 1/3 X 1/3 = 1/27 2. Express the following whole numbers using exponents: a. 4 = 22 b. 16 = 42 c. 125 = 53 d. 100 = 102 e. 10,000 = 104 f. 0.001 = 10 -3 g. 0.0000001 = 10 -7 h. 10 = 101 i. Is there more than one answer to any of the problems in 2? Explain your answer. Yes. For example, 16 = 24 AND 42. 3. Convert the following numbers to scientific notation: a. 100.0 =1.000 X 102 b. 4.567 = 4.567 x 100 c. 345.000 = 3.45000 x 102_ d. 100,000,000,000 = 1 x 1011 2 e. 0.078 = 7.8 X 10 -2 f. 5,876,908,000 = 5.876908 X 109 4. Convert the following numbers to standard notation: a. 123 X 102 = 12300 b. 0.456 X 103 = 456 c. 4.00 X 10 –5 = 0.0000400 d. 100 X 10 –3 = 0.100 6 e. 0.0056 X 10 = 5600 5. Fill in the blanks so that the numers on both sides of the = sign are equal: 2.58 X 10-2 = 25.8 X 10 –3 .4 a. 0.050 X 10 –3 = 0.50 X10 = 5.0 X 10-5 = 500 X 10-7 b. 15.0 X 103 = 150 X 102 = 150,000 X 10 –1 = 150,000,000 X 10–4 c. 54 x 10 –2 = 5.4 X 10-1 d. 10000 X 101 = 1.0000 X 105 e. f. g. h. i. 6. 7. 8. 9. 78 X 1012 = 7.8 X 1013 0.0023 X 102 = 0.00000023 X 106 4.56 x 1010 = 45600 X 106 25 X 10 –4 = 250 X 10 –5 98.901 X 10 –3 = 0.0098901 X 101 j. 0.00098 X 10 –2 = 9.8 x 10-6 Explain how you figured out the answer to 5g: The exponent is smaller than 10; move the decimal 4 places to the right. What strategy can you use to check your answers to problem 4 to see that they are correct? Use a calculator. Which question did you find the most difficult? Why? Is there any concept covered in this assignment that you do not understand? If so, what can you do to better master the material?