6.56 Given $\lg 2=0.3010, \lg 3=0.4771$, then the number of digits after the decimal point when the first non-zero digit appears in $\left(\frac{6}{25}\right)^{100}$ is
(A) 61.
(B) 62.
(C) 63.
(D) None of the above.
(Shanghai Junior High School Mathematics Competition, 1984)
[Solution] Let $x=\left(\frac{6}{25}\right)^{100}$, taking the logarithm we have
$$
\begin{aligned}
\lg x & =100 \lg \frac{6}{25}=100 \lg \frac{2^{3} \cdot 3}{100}=100(3 \lg 2+\lg 3-\lg 100) \\
& =-61.99=\overline{62} .01,
\end{aligned}
$$

we know that $x$ has its first non-zero digit at the 62nd position after the decimal point. Therefore, the answer is $(B)$.