8. (10 points) If the expression $\frac{1}{1 \times 2}-\frac{1}{3 \times 4}+\frac{1}{5 \times 6}-\frac{1}{7 \times 8}+\cdots \frac{1}{2007 \times 2008}+\frac{1}{2009 \times 2010}$ is converted to a decimal, then the first digit after the decimal point is $\qquad$
8. (10 points) If the value of the expression $\frac{1}{1 \times 2}-\frac{1}{3 \times 4}+\frac{1}{5 \times 6}-\frac{1}{7 \times 8}+\cdots \frac{1}{2007 \times 2008}+\frac{1}{2009 \times 2010}$ is converted to a decimal, then the first digit after the decimal point is $\qquad$ .
【Analysis】Based on the periodicity of the addition and subtraction of the fractional sequence, group the fractional sequence to find approximate values, and perform estimation.
【Solution】Solution: $\frac{1}{1 \times 2}-\frac{1}{3 \times 4} \approx 0.41$.
$$
\begin{array}{l}
\frac{1}{5 \times 6}-\frac{1}{7 \times 8} \approx 0.01548 \\
\frac{1}{9 \times 10}-\frac{1}{11 \times 12} \approx 0.0035 \\
\frac{1}{13 \times 14}-\frac{1}{15 \times 16} \approx 0.00133 \\
\frac{1}{17 \times 18}-\frac{1}{19 \times 20} \approx 0.00063
\end{array}
$$
‥Reasoning that the difference between every two fractions becomes closer to 0, and since it is a finite sum, the first digit after the decimal point is 4. Therefore, the answer is: 4.