1. (10 points) $A$ and $B$ are both decimals less than 1, the result of the expression $A \times B + 0.1$ ( )
A. Greater than 1
B. Less than 1
C. Equal to 1
D. Cannot determine the relationship with 1
【Analysis】According to the problem and the rules of decimal multiplication, it is known that the product of $A \times B$ should be a number greater than 0 and less than 1. Therefore, the sum of $A \times B+0.1$ should be a number greater than 0.1 and less than 1.1, i.e., $0.1<A \times B+0.1<1.1$. Thus, the answer is clear.

【Solution】Since $A$ and $B$ are both decimals less than 1
$$
\begin{array}{l}
\therefore 0<A \times B<1 \\
0+0.1<A \times B+0.1<1+0.1 \\
0.1<A \times B+0.1<1.1
\end{array}
$$
The sum of $A \times B+0.1$ could be greater than 1, less than 1, or equal to 1, i.e., it is impossible to determine the size relative to 1.
Therefore, the correct choice is: $D$.