［Solution］Let $x=0.01^{0.01}$, then we have
$$
\lg x=0.01 \lg 0.01=0.01 \lg 10^{-2}=-0.02 \text {, }
$$

Also, $\lg a=\overline{1} .02=-1+0.02$, then $1+\lg a=0.02$, which means $\lg 10 a=0.02$.
$\therefore \quad \lg x=-\lg 10 a$, then $x=\frac{1}{10 a}$. Therefore, the answer is $(D)$.
6.51 Given $\lg a=\overline{1} .02$, then the value of $0.01^{0.01}$ is 
(A) $a$.
(B) $\frac{1}{a}$.
(C) $10 a$.
(D) $\frac{1}{10 a}$
(China Guangzhou, Wuhan, Fuzhou and other five cities Junior High School Mathematics League, 1985;
China Shanghai Junior High School Mathematics Competition, 1986)