B. On the blackboard, there are
$$
1, \frac{1}{2}, \cdots, \frac{1}{100}
$$

a total of 100 numbers. Each operation involves selecting two numbers $a$ and $b$ from the numbers on the blackboard, then deleting $a$ and $b$, and writing the number $a+b+a b$ on the blackboard. After 99 operations, the number left on the blackboard is ( ).
(A) 2012
(B) 101
(C) 100
(D) 99
B. C.

Since $a+b+a b+1=(a+1)(b+1)$, the product of each number on the blackboard plus 1 remains unchanged before and after each operation.

Let the number left on the blackboard after 99 operations be $x$. Then
$$
\begin{array}{l}
x+1=(1+1)\left(\frac{1}{2}+1\right) \cdots \cdots\left(\frac{1}{100}+1\right) \\
=101 \\
\Rightarrow x=100 .
\end{array}
$$