Estimation and Approximation Techniques: Notes and 100 Practice Questions

 

Estimation and Approximation Techniques: Notes and 100 Practice Questions

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Estimation and Approximation: Essential Notes

What is Estimation?

Estimation is the process of quickly finding a value that is close enough to the correct answer, usually by rounding numbers and simplifying calculations. It is a vital skill in competitive exams for saving time and eliminating unlikely options54.

Why Use Estimation?

• Speed: Helps solve questions faster, especially under time pressure.

• Accuracy: Useful for verifying calculations and identifying potential errors.

• Elimination: Makes it easier to rule out incorrect options in multiple-choice questions5.

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Key Estimation Techniques

1. Rounding Numbers

• Round numbers to the nearest 10, 100, or 1000 as appropriate before performing operations.

• Example: $78\approx 80$, $143\approx 140$56.

2. Compatible Numbers

• Use numbers that are easy to compute mentally.

• Example: For $198÷4$, estimate as $200÷4=50$.

3. Front-End Estimation

• Use only the leading digits for a quick estimate.

• Example: $456+378\approx 400+300=700$.

4. Clustering

• When numbers are close, multiply or add one representative value by the count.

• Example: $49+52+51\approx 3\times 50=150$.

5. Estimating with Multiplication

• Round each factor before multiplying.

• Example: $31\times 59\approx 30\times 60=1800$ (actual: 1829)5.

6. Estimating Square Roots

• Find perfect squares close to the number.

• Example: $\sqrt{68}$ is between $\sqrt{64}=8$ and $\sqrt{81}=9$, so estimate as $8.2$2.

7. Approximate Calculations in Simplification

• For complex multiplications, use place value tricks or break numbers for easier calculation12.

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Examples

Example 1:
Estimate $47\times 19$
Round: $50\times 20=1000$ (actual: 893)

Example 2:
Estimate $378+624$
Round: $400+600=1000$ (actual: 1002)

Example 3:
Estimate $\sqrt{50}$
Between $\sqrt{49}=7$ and $\sqrt{64}=8$, so estimate $\approx 7.1$

Example 4:
Estimate $145÷7$
Round: $140÷7=20$

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Tips for Fast Estimation in Exams

• Always round numbers before calculation.

• Use estimation to quickly check if your answer is reasonable.

• If options are far apart, estimation is usually enough to find the answer.

• For close options, estimate first, then do a quick check with actual calculation if needed542.

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100 Practice Questions on Estimation and Approximation

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Questions 1–20 (with solutions)

1. Estimate $29\times 41$
   Ans: $30\times 40=1200$

2. Estimate $378+624$
   Ans: $400+600=1000$

3. Estimate $145÷7$
   Ans: $140÷7=20$

4. Estimate $\sqrt{50}$
   Ans: Between $\sqrt{49}=7$ and $\sqrt{64}=8$, so $\approx 7.1$

5. Estimate $82\times 19$
   Ans: $80\times 20=1600$

6. Estimate $99+101+98$
   Ans: $3\times 100=300$

7. Estimate $253÷12$
   Ans: $240÷12=20$

8. Estimate $67\times 33$
   Ans: $70\times 30=2100$

9. Estimate $487+312$
   Ans: $500+300=800$

10. Estimate $399÷8$
    Ans: $400÷8=50$

11. Estimate $\sqrt{90}$
    Ans: Between $\sqrt{81}=9$ and $\sqrt{100}=10$, so $\approx 9.5$

12. Estimate $56\times 22$
    Ans: $60\times 20=1200$

13. Estimate $789+212$
    Ans: $800+200=1000$

14. Estimate $158÷4$
    Ans: $160÷4=40$

15. Estimate $\sqrt{115}$
    Ans: Between $\sqrt{100}=10$ and $\sqrt{121}=11$, so $\approx 10.7$

16. Estimate $43\times 58$
    Ans: $40\times 60=2400$

17. Estimate $673+329$
    Ans: $700+300=1000$

18. Estimate $299÷6$
    Ans: $300÷6=50$

19. Estimate $\sqrt{35}$
    Ans: Between $\sqrt{25}=5$ and $\sqrt{36}=6$, so $\approx 5.9$

20. Estimate $84\times 17$
    Ans: $80\times 20=1600$

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Questions 21–100 (Practice Only)

21. Estimate $56\times 49$

22. Estimate $123+478$

23. Estimate $378÷9$

24. Estimate $\sqrt{120}$

25. Estimate $89\times 21$

26. Estimate $225+376$

27. Estimate $541÷13$

28. Estimate $72\times 18$

29. Estimate $399+601$

30. Estimate $288÷7$

31. Estimate $\sqrt{75}$

32. Estimate $61\times 29$

33. Estimate $487+312$

34. Estimate $159÷8$

35. Estimate $\sqrt{82}$

36. Estimate $37\times 54$

37. Estimate $673+329$

38. Estimate $199÷4$

39. Estimate $\sqrt{45}$

40. Estimate $92\times 13$

41. Estimate $68\times 41$

42. Estimate $781+219$

43. Estimate $253÷11$

44. Estimate $\sqrt{58}$

45. Estimate $73\times 32$

46. Estimate $399+501$

47. Estimate $158÷5$

48. Estimate $\sqrt{110}$

49. Estimate $42\times 27$

50. Estimate $84\times 19$

51. Estimate $299+701$

52. Estimate $168÷7$

53. Estimate $\sqrt{72}$

54. Estimate $53\times 68$

55. Estimate $487+312$

56. Estimate $189÷6$

57. Estimate $\sqrt{95}$

58. Estimate $77\times 24$

59. Estimate $673+329$

60. Estimate $299÷5$

61. Estimate $\sqrt{40}$

62. Estimate $84\times 15$

63. Estimate $399+601$

64. Estimate $158÷8$

65. Estimate $\sqrt{105}$

66. Estimate $63\times 29$

67. Estimate $487+312$

68. Estimate $199÷6$

69. Estimate $\sqrt{60}$

70. Estimate $92\times 11$

71. Estimate $68\times 38$

72. Estimate $781+219$

73. Estimate $253÷12$

74. Estimate $\sqrt{78}$

75. Estimate $73\times 28$

76. Estimate $399+501$

77. Estimate $158÷7$

78. Estimate $\sqrt{112}$

79. Estimate $42\times 29$

80. Estimate $84\times 18$

81. Estimate $299+701$

82. Estimate $168÷8$

83. Estimate $\sqrt{85}$

84. Estimate $53\times 62$

85. Estimate $487+312$

86. Estimate $189÷8$

87. Estimate $\sqrt{92}$

88. Estimate $77\times 22$

89. Estimate $673+329$

90. Estimate $299÷7$

91. Estimate $\sqrt{38}$

92. Estimate $84\times 16$

93. Estimate $399+601$

94. Estimate $158÷6$

95. Estimate $\sqrt{108}$

96. Estimate $63\times 31$

97. Estimate $487+312$

98. Estimate $199÷5$

99. Estimate $\sqrt{52}$

100. Estimate $92\times 12$

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Tip:
Practice these estimation techniques daily to improve speed and accuracy in competitive exams. Use estimation first to eliminate options, then calculate precisely if needed542