Find the length to three significant digits of the arc intercepted by a central angle $\theta$ in a circle of radius $r$.
\[
r=16.6 \text { in. } \theta=319^{\circ}
\]
The length of the intercepted arc is approximately in.

Step 1 ：The length of an arc in a circle is given by the formula \(s = r\theta\), where \(s\) is the arc length, \(r\) is the radius of the circle, and \(\theta\) is the central angle in radians. However, the given angle is in degrees. Therefore, we first need to convert the angle from degrees to radians. The conversion factor is \(\frac{\pi}{180}\).

Step 2 ：Given that the radius \(r = 16.6\) inches and the central angle \(\theta = 319^\circ\), we convert the angle to radians to get \(\theta = 5.567600313861911\) radians.

Step 3 ：Substitute the values into the formula to find the arc length. \(s = r\theta = 16.6 \times 5.567600313861911 = 92.42216521010774\) inches.

Step 4 ：The question asks for the length to three significant digits. Therefore, we need to round the result to three significant digits to get \(s = 92.422\) inches.

Step 5 ：Final Answer: The length of the intercepted arc is approximately \(\boxed{92.422}\) inches.