1.5E: Exercises
Practice Makes Perfect
Round Decimals
In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.
1. \(5.781\)
- Answer
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ⓐ \(5.78\) ⓑ \(5.8\) ⓒ \(6\)
2. \(1.638\)
3. \(0.299\)
- Answer
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ⓐ \(0.30\) ⓑ \(0.3\) ⓒ \(0\)
4. \(0.697\)
5. \(63.479\)
- Answer
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ⓐ \(63.48\) ⓑ \(63.5\) ⓒ \(63\)
6. \(84.281\)
Add and Subtract Decimals
In the following exercises, add or subtract.
7. \(−16.53−24.38\)
- Answer
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\(−40.91\)
8. \(−19.47−32.58\)
9. \(−38.69+31.47\)
- Answer
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\(−7.22\)
10. \(−29.83+19.76\)
11. \(72.5-100\)
- Answer
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\(-27.5\)
12. \(86.2-100\)
13. \(91.75−(−10.462)\)
- Answer
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\(02.212\)
14. \(94.69−(−12.678)\)
15. \(55.01−3.7\)
- Answer
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\(51.31\)
16. \(59.08−4.6\)
17. \(2.51−7.4\)
- Answer
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\(−4.89\)
18. \(3.84−6.1\)
Multiply and Divide Decimals
In the following exercises, multiply.
19. \(94.69−(−12.678)\)
- Answer
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\(−11.653\)
20. \((−8.5)(1.69)\)
21. \((−5.18)(−65.23)\)
- Answer
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\(337.8914\)
22. \((−9.16)(−68.34)\)
23. \((0.06)(21.75)\)
- Answer
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\(1.305\)
24. \((0.08)(52.45)\)
25. \((9.24)(10)\)
- Answer
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\(92.4\)
26. \((6.531)(10)\)
27. \((0.025)(100)\)
- Answer
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\(2.5\)
28. \((0.037)(100)\)
29. \((55.2)(1000)\)
- Answer
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\(55200\)
30. \((99.4)(1000)\)
In the following exercises, divide. Round money monetary answers to the nearest cent.
31. \($117.25÷48\)
- Answer
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\($2.44\)
32. \($109.24÷36\)
33. \(1.44÷(−0.3)\)
- Answer
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\(−4.8\)
34. \(−1.15÷(−0.05)\)
35. \(5.2÷2.5\)
- Answer
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\(2.08\)
36. \(14÷0.35\)
Convert Decimals, Fractions and Percents
In the following exercises, write each decimal as a fraction.
37. \(0.04\)
- Answer
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\(\frac{1}{25}\)
38. \(1.464\)
39. \(0.095\)
- Answer
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\(\frac{19}{200}\)
40. \(−0.375\)
In the following exercises, convert each fraction to a decimal.
41. \(\frac{17}{20}\)
- Answer
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\(0.85\)
42. \(\frac{17}{4}\)
43. \(−\frac{310}{25}\)
- Answer
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\(−12.4\)
44. \(−\frac{18}{11}\)
In the following exercises, convert each percent to a decimal.
45. \(71 \%\)
- Answer
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\(0.71\)
46. \(150 \%\)
47. \(39.3 \% \)
- Answer
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\(0.393\)
48. \(7.8 \% \)
In the following exercises, convert each decimal to a percent.
49. \(1.56\)
- Answer
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\(156 \% \)
50. \(3\)
51. \(0.0625\)
- Answer
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\(6.25 \% \)
52. \(2.254\)
Simplify Expressions with Square Roots
In the following exercises, simplify.
53. \(\sqrt{64}\)
- Answer
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\(8\)
54. \(\sqrt{169}\)
55. \(\sqrt{144}\)
- Answer
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\(12\)
56. \(−\sqrt{4}\)
57. \(−\sqrt{100}\)
- Answer
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\(−10\)
58. \(−\sqrt{121}\)
Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers
In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.
59. \(−8,0,1.95286...,\frac{12}{5},\sqrt{36},9\)
- Answer
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ⓐ Whole numbers: \(0,\sqrt{36},9\)
ⓑ Integers: \(−8,0,\sqrt{36},9\)
ⓒ Rational numbers: \(−8,0,\sqrt{36},9\)
ⓓ Irrational numbers: \(1.95286...,\)
ⓔ Real numbers: \(−8,0,1.95286...,\frac{12}{5},\sqrt{36},9\)
60. \(−9,−3\frac{4}{9},−\sqrt{9},0.40 \overline{9},\frac{11}{6},7\)
61. \(−\sqrt{100},−7,−\frac{8}{3},−1,0.77,3\frac{1}{4}\)
- Answer
-
ⓐ Whole numbers: none
ⓑ Integers: \(−\sqrt{100},−7,−1\)
ⓒ Rational numbers: \(−\sqrt{100},−7,−\frac{8}{3},−1,0.77,3\frac{1}{4}\)
ⓓ Irrational numbers: none
ⓔ Real numbers: \(−\sqrt{100},−7,−\frac{8}{3},−1,0.77,3\frac{1}{4}\)
62. \(−6,−\frac{5}{2},0,0. \overline{714285},2\frac{1}{5},\sqrt{14}\)
Locate Fractions and Decimals on the Number Line
In the following exercises, locate the numbers on a number line.
63. \(\frac{3}{10},\frac{7}{2},\frac{11}{6},4\)
- Answer
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64. \(\frac{7}{10},\frac{5}{2},\frac{13}{8},3\)
65. \(\frac{3}{4},−\frac{3}{4},1\frac{2}{3},−1\frac{2}{3},\frac{5}{2},−\frac{5}{2}\)
- Answer
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66. \(\frac{2}{5},−\frac{2}{5},1\frac{3}{4},−1\frac{3}{4},\frac{8}{3},−\frac{8}{3}\)
67. ⓐ \(0.8\) ⓑ \(−1.25\)
- Answer
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68. ⓐ \(−0.9\) ⓑ \(−2.75\)
69. ⓐ \(−1.6\) ⓑ \(3.25\)
- Answer
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70. ⓐ \(3.1\) ⓑ \(−3.65\)
Writing Exercises
71. How does knowing about U.S. money help you learn about decimals?
- Answer
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Answers will vary.
72. When the Szetos sold their home, the selling price was 500% of what they had paid for the house 30 years ago. Explain what 500% means in this context.Szetos sold their home, the selling price was 500% of what they had paid for the house 30 years ago. Explain what 500% means in this context.
73. In your own words, explain the difference between a rational number and an irrational number.
- Answer
-
Answers will vary.
74. Explain how the sets of numbers (counting, whole, integer, rational, irrationals, reals) are related to each other.
Self Check
ⓐ Use this checklist to evaluate your mastery of the objectives of this section.
ⓑ On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?