Find the length to three significant digits of the arc intercepted by a central angle $\theta$ in a circle of radius $r$. $r=10.2 \mathrm{~cm}, \theta=\frac{7 \pi}{5}$ radians
The length of the intercepted arc is approximately dim. (Round to one decimal place as needed.)

Step 1 ：We are given the radius of the circle, \(r = 10.2\) cm, and the central angle, \(\theta = \frac{7\pi}{5}\) radians.

Step 2 ：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.

Step 3 ：Substitute the given values into the formula to find the length of the arc: \(s = 10.2 \times \frac{7\pi}{5}\).

Step 4 ：After calculating the arc length and rounding to one decimal place, we find that \(s \approx 44.9\) cm.

Step 5 ：Final Answer: The length of the intercepted arc is approximately \(\boxed{44.9}\) cm.