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Question

Find approximate value of $$(0.99)^{\frac{2}{3}}$$.


A
0.9949
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B
0.9983
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C
0.9933
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D
0.9911
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Solution

The correct option is C $$0.9933$$
The approximate value of $${(1+x)}^{n}$$ for $$x<1$$ is $$1+nx$$
$${(1-0.01)}^{\frac{2}{3}}$$ $$=1-$$ $$\dfrac{2}{3}\times(0.01)$$ $$=0.9933$$
Thus approximate value of $$0.99^{\frac {2}{3}} $$ is $$0.9933$$.

Mathematics

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