1.5E: Mazoezi

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Nov 1, 2022
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- 1.5: Decimals
- 1.6: Mali ya Hesabu halisi

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Mazoezi hufanya kamili

Decimals pande zote

Katika mazoezi yafuatayo, pande zote namba kwa karibu ⓐ mia ⓑ kumi ⓒ idadi nzima.

1. $5.781$

Jibu: ⓐ $5.78$ ⓑ $5.8$ ⓒ $6$

2. $1.638$

3. $0.299$

Jibu: ⓐ $0.30$ ⓑ $0.3$ ⓒ $0$

4. $0.697$

5. $63.479$

Jibu: ⓐ $63.48$ ⓑ $63.5$ ⓒ $63$

6. $84.281$

Kuongeza na Ondoa Decimals

Katika mazoezi yafuatayo, ongeza au uondoe.

7. $−16.53−24.38$

Jibu: $−40.91$

8. $−19.47−32.58$

9. $−38.69+31.47$

Jibu: $−7.22$

10. $−29.83+19.76$

11. $72.5-100$

Jibu: $-27.5$

12. $86.2-100$

13. $91.75−(−10.462)$

Jibu: $02.212$

14. $94.69−(−12.678)$

15. $55.01−3.7$

Jibu: $51.31$

16. $59.08−4.6$

17. $2.51−7.4$

Jibu: $−4.89$

18. $3.84−6.1$

Kuzidisha na Gawanya Decimals

Katika mazoezi yafuatayo, ongeze.

19. $94.69−(−12.678)$

Jibu: $−11.653$

20. $(−8.5)(1.69)$

21. $(−5.18)(−65.23)$

Jibu: $337.8914$

22. $(−9.16)(−68.34)$

23. $(0.06)(21.75)$

Jibu: $1.305$

24. $(0.08)(52.45)$

25. $(9.24)(10)$

Jibu: $92.4$

26. $(6.531)(10)$

27. $(0.025)(100)$

Jibu: $2.5$

28. $(0.037)(100)$

29. $(55.2)(1000)$

Jibu: $55200$

30. $(99.4)(1000)$

Katika mazoezi yafuatayo, ugawanye. Pande zote fedha majibu ya fedha kwa asilimia karibu.

31. $$117.25÷48$

Jibu: $$2.44$

32. $$109.24÷36$

33. $1.44÷(−0.3)$

Jibu: $−4.8$

34. $−1.15÷(−0.05)$

35. $5.2÷2.5$

Jibu: $2.08$

36. $14÷0.35$

Geuza Decimals, Fractions na asilimia

Katika mazoezi yafuatayo, andika kila decimal kama sehemu.

37. $0.04$

Jibu: $\frac{1}{25}$

38. $1.464$

39. $0.095$

Jibu: $\frac{19}{200}$

40. $−0.375$

Katika mazoezi yafuatayo, kubadilisha kila sehemu kwa decimal.

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

Jibu: $0.85$

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

43. $−\frac{310}{25}$

Jibu: $−12.4$

44. $−\frac{18}{11}$

Katika mazoezi yafuatayo, kubadilisha kila asilimia kwa decimal.

45. $71 \%$

Jibu: $0.71$

46. $150 \%$

47. $39.3 \%$

Jibu: $0.393$

48. $7.8 \%$

Katika mazoezi yafuatayo, kubadilisha kila decimal kwa asilimia.

49. $1.56$

Jibu: $156 \%$

50. $3$

51. $0.0625$

Jibu: $6.25 \%$

52. $2.254$

Rahisisha maneno na Mizizi ya Mraba

Katika mazoezi yafuatayo, kurahisisha.

53. $\sqrt{64}$

Jibu: $8$

54. $\sqrt{169}$

55. $\sqrt{144}$

Jibu: $12$

56. $−\sqrt{4}$

57. $−\sqrt{100}$

Jibu: $−10$

58. $−\sqrt{121}$

Tambua Integers, Nambari za busara, Hesabu zisizofaa, na Hesabu halisi

Katika mazoezi yafuatayo, weka namba zote za ⓐ, ⓑ integers, ⓒ namba za busara, ⓓ namba zisizo na maana, ⓔ namba halisi kwa kila seti ya namba.

59. $−8,0,1.95286...,\frac{12}{5},\sqrt{36},9$

Jibu: ⓐ Idadi nzima: $0,\sqrt{36},9$
ⓑ integers: $−8,0,\sqrt{36},9$
ⓒ Nambari za busara: $−8,0,\sqrt{36},9$
ⓓ Idadi isiyo na maana: $1.95286...,$
ⓔ Nambari halisi: $−8,0,1.95286...,\frac{12}{5},\sqrt{36},9$

60. $−9,−3\frac{4}{9},−\sqrt{9},0.40 \overline{9},\frac{11}{6},7$

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

Jibu: ⓐ Idadi nzima: hakuna
ⓑ Integers: $−\sqrt{100},−7,−1$
ⓒ Nambari za busara: $−\sqrt{100},−7,−\frac{8}{3},−1,0.77,3\frac{1}{4}$
ⓓ Idadi isiyo ya kawaida: hakuna
ⓔ Nambari halisi: $−\sqrt{100},−7,−\frac{8}{3},−1,0.77,3\frac{1}{4}$

62. $−6,−\frac{5}{2},0,0. \overline{714285},2\frac{1}{5},\sqrt{14}$

Pata sehemu ndogo na Decimals kwenye Mstari wa Idadi

Katika mazoezi yafuatayo, Pata namba kwenye mstari wa nambari.

63. $\frac{3}{10},\frac{7}{2},\frac{11}{6},4$

Jibu: $Kielelezo kinaonyesha mstari wa namba na namba kuanzia 0 hadi 6. Baadhi ya maadili yanaonyeshwa. Kutoka kushoto kwenda kulia, haya ni: 3 na 10, 11 na 6, 7 na 2 na 4.$

64. $\frac{7}{10},\frac{5}{2},\frac{13}{8},3$

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

Jibu: $Kielelezo kinaonyesha mstari wa nambari na namba zinazoanzia minus 4 hadi 4. Baadhi ya maadili yanaonyeshwa. Kutoka kushoto kwenda kulia, haya ni: minus 5 na 2, minus 1 na theluthi mbili, minus 3 na 4, 3 na 4, 1 na theluthi mbili, na 5 na 2.$

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

67. ⓐ $0.8$ ⓑ $−1.25$

Jibu: $Kielelezo kinaonyesha mstari wa nambari na namba zinazoanzia minus 4 hadi 4. Maadili mawili yanaonyeshwa. Moja ni kati ya minus 2 na minus 1. Nyingine ni kati ya 0 na 1.$

68. ⓐ $−0.9$ ⓑ $−2.75$

69. ⓐ $−1.6$ ⓑ $3.25$

Jibu: $Kielelezo kinaonyesha mstari wa nambari na namba zinazoanzia minus 4 hadi 4. Maadili mawili yanaonyeshwa. Moja ni kati ya minus 2 na minus 1. Nyingine ni kati ya 3 na 4.$

70. ⓐ $3.1$ ⓑ $−3.65$

Mazoezi ya kuandika

71. Je, kujua kuhusu pesa za Marekani kukusaidia kujifunza kuhusu decimals?

Jibu: Majibu yatatofautiana.

72. Wakati Szetos walipouza nyumba zao, bei ya kuuza ilikuwa 500% ya yale waliyoyolipia nyumba hiyo miaka 30 iliyopita. Eleza nini 500% ina maana katika muktadha huu.Szetos waliuza nyumba zao, bei ya kuuza ilikuwa 500% ya yale waliyoyolipia nyumba 30 iliyopita. Eleza nini 500% ina maana katika muktadha huu.

73. Kwa maneno yako mwenyewe, kuelezea tofauti kati ya nambari ya busara na nambari isiyo na maana.

Jibu: Majibu yatatofautiana.

74. Eleza jinsi seti ya namba (kuhesabu, nzima, integer, busara, irrationals, reals) zinahusiana na kila mmoja.

Self Check

ⓐ Tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

$Jedwali hili lina nguzo 4, safu 6 na mstari wa kichwa. Mstari wa kichwa huandika kila safu: Naweza, kwa ujasiri, kwa msaada na hapana, siipati. Taarifa katika safu ya kwanza ni: decimals pande zote, kuongeza na kuondoa decimals, kuzidisha na kugawanya decimals, kubadilisha decimals, sehemu na asilimia, kurahisisha maneno na mizizi mraba, kutambua integers, namba busara, idadi irrational na idadi halisi, Machapisho sehemu na decimals kwa idadi mstari. Nguzo zilizobaki ni tupu.$

ⓑ Kwa kiwango cha 1-10, ungewezaje kupima ujuzi wako wa sehemu hii kwa kuzingatia majibu yako kwenye orodha? Unawezaje kuboresha hii?