2. Given that the decimal part of $\lg x$ is $a$. Then the decimal part of $\lg \frac{1}{x^{2}}$ is ( ).
(A) $-2 a$
(B) $1-2 a$
(C) $2-2 a$
(D) None of the above
2.D.

Let $\lg x=N+a(N$ be an integer, $0 \leqslant a<1)$, then $\lg \frac{1}{x^{2}}$ $=-2 N-2 a$ and the fractional part of $\lg \frac{1}{x^{2}}$ is
$$
\left\{\begin{array}{ll}
-2 a, & a=0 ; \\
1-2 a, & 0<a \leqslant \frac{1}{2} \\
2-2 a, & \frac{1}{2}<a<1 .
\end{array}\right.
$$