2. (5 points) If twice a number minus half of the number equals 2013, then the number is $\qquad$
【Analysis】Twice a number minus half of this number, is actually this number's $2-\frac{1}{2}=1 \frac{1}{2}$. According to the meaning of division, the problem can be solved.

【Solution】Solution: $2013 \div\left(2-\frac{1}{2}\right)$
$$
\begin{array}{l}
=2013 \div 1 \frac{1}{2} \\
=1342 ;
\end{array}
$$

Answer: The number is 1342.
Therefore, the answer is: 1342.
【Comment】The key to solving this problem is to understand: twice a number minus half of this number, is actually finding this number's $2-\frac{1}{2}=1 \frac{1}{2}$.