8、Write the first two decimal places of the product $\underbrace{\frac{2}{3} \times \frac{2}{3} \times \cdots \times \frac{2}{3}}_{10 \overbrace{}^{2}}$ when expressed as a decimal. $\qquad$
8. Solution: Notice that $2^{5}=32>27=3^{3}$, so $\frac{2^{3}}{3^{3}}>\frac{1}{2^{2}}, \frac{2^{9}}{3^{9}}>\frac{1}{2^{6}}$, thus $\frac{2^{10}}{3^{10}}>\frac{1}{2^{6}} \times \frac{2}{3}=\frac{1}{2^{5} \times 3}=\frac{1}{96}>\frac{1}{100}=0.01$.

Also, $5 \times 2^{4}=80<81=3^{4}$, so $\frac{2^{4}}{3^{4}}<\frac{1}{5}, \frac{2^{8}}{3^{8}}<\frac{1}{25}$.
Therefore, $\frac{2^{10}}{3^{10}}<\frac{1}{25} \times \frac{2^{2}}{3^{2}}<\frac{1}{25} \times \frac{1}{2}=\frac{1}{50}=0.02$.