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# 1.5E: Exercises

• • OpenStax
• OpenStax
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## Practice Makes Perfect

Round Decimals

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

1. $$5.781$$

ⓐ $$5.78$$ ⓑ $$5.8$$ ⓒ $$6$$

2. $$1.638$$

3. $$0.299$$

ⓐ $$0.30$$ ⓑ $$0.3$$ ⓒ $$0$$

4. $$0.697$$

5. $$63.479$$

ⓐ $$63.48$$ ⓑ $$63.5$$ ⓒ $$63$$

6. $$84.281$$

In the following exercises, add or subtract.

7. $$−16.53−24.38$$

$$−40.91$$

8. $$−19.47−32.58$$

9. $$−38.69+31.47$$

$$−7.22$$

10. $$−29.83+19.76$$

11. $$72.5-100$$

$$-27.5$$

12. $$86.2-100$$

13. $$91.75−(−10.462)$$

$$02.212$$

14. $$94.69−(−12.678)$$

15. $$55.01−3.7$$

$$51.31$$

16. $$59.08−4.6$$

17. $$2.51−7.4$$

$$−4.89$$

18. $$3.84−6.1$$

Multiply and Divide Decimals

In the following exercises, multiply.

19. $$94.69−(−12.678)$$

$$−11.653$$

20. $$(−8.5)(1.69)$$

21. $$(−5.18)(−65.23)$$

$$337.8914$$

22. $$(−9.16)(−68.34)$$

23. $$(0.06)(21.75)$$

$$1.305$$

24. $$(0.08)(52.45)$$

25. $$(9.24)(10)$$

$$92.4$$

26. $$(6.531)(10)$$

27. $$(0.025)(100)$$

$$2.5$$

28. $$(0.037)(100)$$

29. $$(55.2)(1000)$$

$$55200$$

30. $$(99.4)(1000)$$

In the following exercises, divide. Round money monetary answers to the nearest cent.

31. $$117.25÷48$$

$$2.44$$

32. $$109.24÷36$$

33. $$1.44÷(−0.3)$$

$$−4.8$$

34. $$−1.15÷(−0.05)$$

35. $$5.2÷2.5$$

$$2.08$$

36. $$14÷0.35$$

Convert Decimals, Fractions and Percents

In the following exercises, write each decimal as a fraction.

37. $$0.04$$

$$\frac{1}{25}$$

38. $$1.464$$

39. $$0.095$$

$$\frac{19}{200}$$

40. $$−0.375$$

In the following exercises, convert each fraction to a decimal.

41. $$\frac{17}{20}$$

$$0.85$$

42. $$\frac{17}{4}$$

43. $$−\frac{310}{25}$$

$$−12.4$$

44. $$−\frac{18}{11}$$

In the following exercises, convert each percent to a decimal.

45. $$71 \%$$

$$0.71$$

46. $$150 \%$$

47. $$39.3 \%$$

$$0.393$$

48. $$7.8 \%$$

In the following exercises, convert each decimal to a percent.

49. $$1.56$$

$$156 \%$$

50. $$3$$

51. $$0.0625$$

$$6.25 \%$$

52. $$2.254$$

Simplify Expressions with Square Roots

In the following exercises, simplify.

53. $$\sqrt{64}$$

$$8$$

54. $$\sqrt{169}$$

55. $$\sqrt{144}$$

$$12$$

56. $$−\sqrt{4}$$

57. $$−\sqrt{100}$$

$$−10$$

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. $$−8,0,1.95286...,\frac{12}{5},\sqrt{36},9$$

ⓐ 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. $$−\sqrt{100},−7,−\frac{8}{3},−1,0.77,3\frac{1}{4}$$

ⓐ 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. $$\frac{3}{10},\frac{7}{2},\frac{11}{6},4$$ 64. $$\frac{7}{10},\frac{5}{2},\frac{13}{8},3$$

65. $$\frac{3}{4},−\frac{3}{4},1\frac{2}{3},−1\frac{2}{3},\frac{5}{2},−\frac{5}{2}$$ 66. $$\frac{2}{5},−\frac{2}{5},1\frac{3}{4},−1\frac{3}{4},\frac{8}{3},−\frac{8}{3}$$

67. ⓐ $$0.8$$ ⓑ $$−1.25$$ 68. ⓐ $$−0.9$$ ⓑ $$−2.75$$

69. ⓐ $$−1.6$$ ⓑ $$3.25$$ 70. ⓐ $$3.1$$ ⓑ $$−3.65$$

## Writing Exercises

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.

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?

1.5E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.