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Question

The approximate value of (7.995)13 correct to four decimal places is


A

1.9995

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B

1.9996

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C

1.9990

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D

1.9991

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Solution

The correct option is A

1.9995


(7.995)13 = (80.005)13 = (8)13 [10.0058]13

= 2[1 - 13 × 0.0058 + 13(131)2+1 (0.0058)2 + ............]

= 2[1 - 0.00524 - 13×131 × \(\frac{(0.005)^2}{8} + ......... ]\)

=2(10.000208)=2×0.999792=1.9995


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