By Douglas R. Hofstadter
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Extra info for Goedel, Escher, Bach.. an eternal golden braid
Sample text
A graph of the real numbers is shown on a number line by shading all points as in Fig. 9. All rational numbers are real numbers, but there are points on the number line that do not correspond to rational numbers. Those real numbers that are not rational are called irrational. An irrational number cannot be written as a ratio of integers. It can be shown that numbers such as ͙2ෆ (the square root of 2) and (Greek letter pi) are irrational. The number ͙2ෆ is a number that can ෆ ϭ 2). The number is the ratio of the be multiplied by itself to obtain 2 (͙2ෆ и ͙2 circumference and diameter of any circle.
13 50 19. ᎏᎏ 100 5 20. ᎏᎏ 1000 200 21. ᎏᎏ 100 125 22. ᎏᎏ 100 18 23. ᎏᎏ 48 34 24. ᎏᎏ 102 26 25. ᎏᎏ 42 70 26. ᎏᎏ 112 84 27. ᎏᎏ 91 121 28. ᎏᎏ 132 U3V Unit Conversion Perform the indicated unit conversions. See Example 4. Round approximate answers to the nearest hundredth. Answers can vary slightly depending on the conversion factors used. 41. 42. 43. 44. 45. 46. 47. 48. 49. Convert 96 feet to inches. Convert 33 yards to feet. 22 miles to kilometers. 6 kilometers to miles. 5 centimeters to inches.
42. 43. 44. 45. 46. 47. 48. 49. Convert 96 feet to inches. Convert 33 yards to feet. 22 miles to kilometers. 6 kilometers to miles. 5 centimeters to inches. 1 inches to centimeters. 2 ounces to grams. Convert 233 grams to ounces. Convert 40 miles per hour to feet per second. 50. Convert 200 feet per second to miles per hour. 51. Convert 500 feet per second to kilometers per hour. 52. Convert 230 yards per second to miles per minute. qxd 9/14/10 9:45 AM Page 24 24 1-24 Chapter 1 Real Numbers and Their Properties U4V Dividing Fractions 83.