The circumference \( C \) of a circle is calculated using the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.
Given that the radius \( r \) is 38 inches and using \( \pi \approx 3.14 \):
\[ C = 2 \times 3.14 \times 38 \]
Now, performing the calculation:
\[ C = 2 \times 3.14 = 6.28 \]
\[ C = 6.28 \times 38 \]
Calculating \( 6.28 \times 38 \):
\[ C = 238.64 \]
Thus, the approximate circumference of the circle to the nearest hundredths is:
\[ \boxed{238.64} \text{ inches} \]