Question

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

A
0.9949
B
0.9983
C
0.9933
D
0.9911

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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