3-2 Rational Numbers ANSWER: 2. 9 ANSWER: 3. ANSWER: 5. ANSWER: 6. ANSWER:
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1 1. Write each number as a fraction Write each decimal as a fraction or mixed number in simplest form MEASUREMENT There are approximately 2.54 centimeters in 1 inch. Express 2.54 as a mixed number. esolutions Manual - Powered by Cognero Page 1
2 Identify all sets to which each number belongs integer, rational rational natural, whole, integer, rational Write each number as a fraction esolutions Manual - Powered by Cognero Page 2
3 Write each decimal as a fraction or mixed number in simplest form esolutions Manual - Powered by Cognero Page 3
4 21. FINANCIAL LITERACY Recently, one U.S. dollar was equal to British pounds. Express as a fraction. 22. POPULATION The estimated portions for various age groups of the population for 2010 are shown in the table. a. Find the fraction of the population that is 19 years of age or younger. b. Find the fraction of the population that is 20 to 64 years of age. a. b. 23. Write each decimal as a fraction or mixed number in simplest form esolutions Manual - Powered by Cognero Page 4
5 Identify all sets to which each number belongs integer, rational natural, whole, integer, rational rational rational irrational irrational esolutions Manual - Powered by Cognero Page 5
6 35. JEWELRY Maria has a bead that is 0.6 inch long. She wants to use the bead to fill a space that is inch long. Will the bead fit? Explain. Yes; = and > 0.6, so the bead will fit. 36. FOOD All of the Calories in one cup of milk come from fat, protein, and carbohydrates. Use the table to find the fraction of Calories that comes from protein. Write the fraction in simplest form. Replace each _ with <, >, or = to make a true sentence _ 0.3 > 38. _ = _ < 40. _ 0.9 < esolutions Manual - Powered by Cognero Page 6
7 41. _ > 42. _ < Write each decimal as a fraction or mixed number in simplest form esolutions Manual - Powered by Cognero Page 7
8 49. MULTIPLE REPRESENTATIONS Pi (π) is a nonrepeating, nonterminating decimal. Two common estimates for pi are 3.14 and. a. Graphical Use a calculator to find the value of π to seven decimal places. Then graph the three values on a number line. b. Symbolic Write an inequality comparing the values. c. Verbal To find the circumference of a circle, you multiply pi by the diameter d of the circle. Explain when you might use 3.14 to find the circumference and when you might use to find the circumference. a b < π < c. Sample answer: If the diameter is a multiple of 7, use. Otherwise, use HISTORY The mathematician Archimedes believed that π was between and. a. Express each mixed number as a decimal rounded to the nearest thousandth. Was Archimedes theory correct? Explain. b. The Rhind Papyrus records that the Egyptians used for π. Express the fraction as a decimal rounded to the nearest thousandth. Which value is closer to the actual value of π, Arcihimedes or the Egyptians value? a , 3.141; yes; Sample answer: Since > > 3.141, pi is between the two values and his theory was correct. b ; Archimedes value is closer than the Egyptians. esolutions Manual - Powered by Cognero Page 8
9 Order each set of rational numbers from least to greatest ,,, 3.38, 3.4,, ,,, 0.32, 0.32,, 53., 1.9,, ,, 1.9, 54.,,, 9.82,, 9.82, 55. ANIMALS A lion s speed is the speed of a cheetah. Find the least rational number with a denominator of 9 that is greater than. Find the greatest rational number with a denominator of 8 that is less than. Write an inequality comparing the three numbers. ; ; esolutions Manual - Powered by Cognero Page 9
10 56. OPEN ENDED Choose a repeating decimal in which three digits repeat. Write the number as a fraction or mixed number in simplest form. Sample answer: WRITING IN MATH Explain why is greater than Sample answer: Since = and 0.76 = , is greater than CHALLENGE Antonio stated that = 1. Show that he is correct. Let N = so, 10N = REASONING Determine whether the following statements are true or false. If true, explain your reasoning. If false, give a counterexample. a. All integers are rational numbers. b. All whole numbers are integers. c. A rational number is always an integer. d. All natural numbers are rational. a. true; Sample answer: Integers include all whole numbers and their opposites. Therefore, they belong to the set of rational numbers. b. true; Sample answer: All whole numbers and their opposites belong to the set of integers. c. false: Sample answer: is not an integer d. true: Sample answer: All natural numbers are rational because they can be expressed as fractions. esolutions Manual - Powered by Cognero Page 10
11 60. WRITING IN MATH How do you compare and order fractions and decimals? Give an example to explain your reasoning. Sample answer: Convert all the numbers to fractions or decimals. Then use a number line to compare. 61. Which fraction is between 0.12 and 0.15? A B C D B 62. Which of the following is not a rational number? F G 4.27 H J J 63. Last football season, Jason made 0.85 of his field goal attempts. Write this decimal as a fraction in simplest form. A B C D C esolutions Manual - Powered by Cognero Page 11
12 64. EXTENDED RESPONSE The table shows the results of a survey about how students get to school. 65. a. Write each decimal in the table as a fraction. b. List the methods of transportation in order from least to greatest. c. Which method of transportation do most students use to get to school? a. bus: ; walk: ; car: ; bicycle: ; other: b. other, bicycle, walk, car, bus c. bus Write each fraction as a decimal. Use a bar to show a repeating decimal esolutions Manual - Powered by Cognero Page 12
13 Graph the figure below and its image after the transformation indicated. 69. translation 3 units down and 2 units left 70. translation 4 units up and 1 unit right esolutions Manual - Powered by Cognero Page 13
14 71. reflection across the x-axis 72. reflection across the y-axis State the domain and range for each relation. 73. {(0, 0), (3, 2), (4, 6), (8, 12)} D = {0, 3, 4, 8}; R = {0, 2, 6, 12} 74. {(1, 2), (3, 4), (5, 6), (7, 8)} D = {1, 3, 5, 7}; R = {2, 4, 6, 8} 75. Mount Kilimanjaro s altitude is 5895 meters. Lake Assal s altitude is 155 meters. Find the difference between these altitudes m esolutions Manual - Powered by Cognero Page 14
15 Find each product ( 12) ( 3)( 4)(0) (5)( 9) ( 20) 280 esolutions Manual - Powered by Cognero Page 15
Chapter Review. Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. 1. SOLUTION: So, = 0.3. SOLUTION: So,.
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