To find the distance around the circular path, we can interpret the information as follows: the half-mile-long sidewalk through the middle represents the diameter of the circle, which is 0.5 miles.
The formula for the circumference \( C \) of a circle is given by:
\[ C = \pi d \]
where \( d \) is the diameter of the circle.
Substituting in \( d = 0.5 \) miles:
\[ C = \pi \times 0.5 \approx 3.14 \times 0.5 \approx 1.57 \text{ miles} \]
Rounding this to one decimal place gives us:
\[ C \approx 1.6 \text{ miles} \]
So, the answer is 1.6 mi.