Step 1: Calculating the Ideal Number of Stations.
The ideal number of rain gauge stations (\(n\)) is found using:
\[n = \left( \frac{C}{E} \right)^2\]
Where:
- \(C\) is the coefficient of variation (29.54% or 0.2954)
- \(E\) is the allowable error (10% or 0.1)
Step 2: Value Substitution.
Insert the values into the formula:
\[n = \left( \frac{0.2954}{0.1} \right)^2 = (2.954)^2 \approx 8.74 \approx 9\]
Step 3: Result.
Therefore, the ideal number of stations is roughly 9, corresponding to option (3).
Final Answer:
\[
\boxed{9}
\]