Question

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

• A. $0.9949$
• B. $0.9983$
• C. $0.9933$
• D. $0.9911$

Answer 1

The correct option is C $0.9933$

The approximate value of ${(1+x)}^n$ for $x<1$ is $1+nx$

${(1-0.01)}^{\frac{2}{3}}$ $=1-$ $\frac{2}{3}\times \left(0.01\right)$ $=0.9933$

Thus approximate value of ${0.99}^{\frac{2}{3}}$ is $0.9933$.