To find the length of arc \( RT \) in circle \( S \) given that \( m \angle RST = 30^\circ \) and the radius \( RS = 17 \) units, we can use the formula for the length of an arc:
\[ L = \frac{\theta}{360^\circ} \times C \]
where \( L \) is the length of the arc, \( \theta \) is the central angle in degrees, and \( C \) is the circumference of the circle.
First, we need to calculate the circumference \( C \) of the circle. The circumference is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius.
Here, the radius \( r = 17 \) units. So,
\[ C = 2\pi(17) = 34\pi \]
Now, we substitute \( \theta = 30^\circ \) into the arc length formula:
\[ L = \frac{30}{360} \times (34\pi) \]
This simplifies to:
\[ L = \frac{1}{12} \times 34\pi \]
Calculating this gives:
\[ L = \frac{34\pi}{12} = \frac{17\pi}{6} \]
Now, to find the numerical value, we can use the approximation \( \pi \approx 3.14 \):
\[ L \approx \frac{17 \times 3.14}{6} \approx \frac{53.38}{6} \approx 8.896666 \]
Rounding this to the nearest hundredth, we find:
\[ L \approx 8.90 \]
Thus, the length of arc \( RT \) is approximately \(\boxed{8.90}\) units.