The gain of the amplifier is \( 1000 \pm 100 \), meaning the gain can vary from 900 to 1100. To keep the gain within \( \pm 10\% \), we need to reduce the variation. The required feedback can be calculated using the formula for feedback, which ensures the gain stays within the desired range:
\[
\text{Feedback factor} = \frac{100}{1000} = 0.099
\]
Thus, the correct feedback factor is 0.099. Therefore, the correct answer is option (1).