274 CHAPTER 5 Number Theory and the Real Number System 70. Computer Speed As of June 2023, the fastest computer in the world was the Hewlett Packard Frontier, run by the U.S. Department of Energy. This computer is capable of performing about 1.194 EFLOPS ( ) × 1.194 1018 calculations per second. At this rate, about how long will it take for this computer to perform a task requiring × 7.6 1065 calculations? Write your answer in scientific notation. × 6.37 10 seconds 47 71. Blood Cells in a Cubic Millimeter If a cubic millimeter of blood contains 5,800,000 red blood cells, how many red blood cells are contained in 50 cubic millimeters of blood? Write your answer in scientific notation. × 2.9 108 cells 72. Bucket Full of Molecules A drop of water contains about 40 billion molecules. If a bucket has half a million drops of water in it, how many molecules of water are in the bucket? Write your answer in scientific notation. × 2.0 1016 molecules 73. Earth to Sun Comparison The mass of the sun is approximately × 210 kilograms, 30 and the mass of Earth is approximately × 610 kilograms. 24 How many times greater is the mass of the sun than the mass of Earth? Write your answer in decimal notation. About333,333 times 74. Radioactive Isotopes The half-life of a radioactive isotope is the time required for half the quantity of the isotope to decompose. The half-life of uranium-238 is × 4.5 10 years, 9 and the half-life of uranium-234 is × 2.5 105 years. How many times greater is the half-life of uranium-238 than uranium-234? 18,000 times 75. Metric System Comparison In the metric system, = 1 meter 103 millimeters. How many times greater is a meter than a millimeter? 1000 76. Milligrams and Kilograms In the metric system, = 1 gram 103 milligrams and = − 1 gram 10 3 kilogram. What is the relationship between milligrams and kilograms? = 1,000,000 mg 1 kg 77. Internet Usage In 2022, Denmark was the country with the largest percentage of its population using the Internet. The population of Denmark was about × 5.88 106 people. If 99% of Denmark’s population used the Internet in 2022, approximately how many people used the Internet? 5,821,200 people m Denmark 78. Smartphone Usage In 2023, there were approximately × 6.92 109 smartphone users worldwide. If the world’s population in 2023 was about × 8.04 10 ,9 determine the approximate percentage of the worldwide population that used a smartphone. ≈86.1% Challenge Problems/Group Activities 79. Comparing a Million to a Billion Many people have no idea of the difference in size between a million (1,000,000), a billion (1,000,000,000), and a trillion (1,000,000,000,000). a) Write a million, a billion, and a trillion in scientific notation. × × × 1 10,1 10,1 10 6 9 12 b) Determine how long it would take to spend one million dollars if you spent $1000 a day. 1000 days (about 2.74 years) c) Repeat part (b) for one billion dollars. 1,000,000 days (about 2739.73 years) d) Repeat part (b) for one trillion dollars. 1,000,000,000 days (about 2,739,726.03 years) e) How many times greater is one billion dollars than one million dollars? 1000 times greater 80. Speed of Light a) Light travels at a speed of × 1.86 10 mi/sec. 5 A lightyear is the distance that light travels in 1 year. Determine the number of miles in a light-year. About × 5.87 10 (or 5.87 trillion) mi 12 b) Earth is approximately 93,000,000 mi from the sun. How long does it take light from the sun to reach Earth? About 500 sec, or 8 min 20 sec 81. Bacteria in a Culture The exponential function = ⋅ E t( ) 2 2t 10 approximates the number of bacteria in a certain culture after t hours. a) The initial number of bacteria is determined when = t 0. What is the initial number of bacteria? 1024 bacteria b) How many bacteria are there after 1 2 hour? ≈1448 bacteria Research Activities 82. U.S. Government Debt Obtain data from the U.S. Department of the Treasury and from the U.S. Bureau of the Census Internet websites to calculate the current U.S. national debt per person. Write a report in which you compare your figure with those obtained in Exercise 61 and Example 12. Include in your report definitions of the following terms: revenues, expenditures, deficit, and surplus. 83. Scientific Notation Find an article that contains scientific notation. Write a paragraph explaining how scientific notation was used. Scanrail/123RF
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