Approximation
Direction: What approximate value should come in place of the question mark(?) in the following question ? (Note that you are not expected to calculate the exact value).
 (9.95)^{2} x (2.01)^{3} = 2 x (?)^{2}

 12
 15
 25
 20

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(9.95)^{2} x (2.01)^{3} = 2 x (?)^{2}
Here, 9.95 is Approximated to 10, 2.01 is approximate to 2 because calculating the square or cubes of whole number is much easier than to calculate the square or cube of decimal numbers
2 x (?) ^{2} = ( 10)^{2} x (2)^{3} = 100 x 8 = 800Correct Option: D
(9.95)^{2} x (2.01)^{3} = 2 x (?)^{2}
Here, 9.95 is Approximated to 10, 2.01 is approximate to 2 because calculating the square or cubes of whole number is much easier than to calculate the square or cube of decimal numbers
2 x (?) ^{2} = ( 10)^{2} x (2)^{3} = 100 x 8 = 800
⇒ (?)^{2} = 400
∴ ? =20
 99.999 ÷ 0.99 ÷ 0.00991234 = ?

 100
 10000
 1000
 100000

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99.999 ÷ 0.99 ÷ 0.00991234 = 100 ÷ 1 ÷ 0.01
Correct Option: B
99.999 ÷ 0.99 ÷ 0.00991234
= 100 ÷ 1 ÷ 0.01 = 10000
 [137 ÷ 17 x 3.99]/[4.02 x 3.98] = ?

 3.2
 3.5
 2.5
 2

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[137 ÷ 17 x 3.99]/[4.02 x 3.98] = ? ≈ (137 ÷ 17 x 4) / (4 x 4)
Correct Option: D
[137 ÷ 17 x 3.99]/[4.02 x 3.98] = ? ≈ (137 ÷ 17 x 4) / (4 x 4) ≈ 2
 95^{3.7} ÷ 95 ^{0.9989 } = 95^{?}

 1.9
 3
 2.99
 2.7

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? = 95^{3.7} ÷ 95^{0.9989} = 95^{?}
⇒ 95^{(3.7  0.9989)} = 95^{?}
⇒ 95^{2.7011} = 95^{?}Correct Option: D
? = 95^{3.7} ÷ 95^{0.9989} = 95^{?}
⇒ 95^{(3.7  0.9989)} = 95^{?}
⇒ 95^{2.7011} = 95^{?}
∴ ? = 2.7011 ≈ 2.7
 3^{7.5}/27^{1.5 } x 9^{2} = 3^{?}

 5
 4.5
 7
 6.50

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3 ^{7.5} ÷ 27^{1.5} x 9^{2} = 3^{?}
⇒ 3^{7.5} ÷ (3)^{3 x 15 } x 3^{2 x 2 } = 3 ^{?}Correct Option: C
3 ^{7.5} ÷ 27^{1.5} x 9^{2} = 3^{?}
⇒ 3^{7.5} ÷ (3)^{3 x 15 } x 3^{2 x 2 } = 3 ^{?}
⇒ 3^{7.5  4.5 + 4} = 3^{?} ⇒ 3^{7} = 3^{?} ⇒ ? = 7