1. **State the problem:** We want to find what percent of 2 radians is $\frac{\pi}{11}$ radians. 2. **Formula:** To find what percent one value is of another, use: $$\text{Percent} = \left(\frac{\text{part}}{\text{whole}}\right) \times 100$$ 3. **Apply the formula:** Here, the part is $\frac{\pi}{11}$ and the whole is 2, so: $$\text{Percent} = \left(\frac{\frac{\pi}{11}}{2}\right) \times 100$$ 4. **Simplify the fraction:** $$\frac{\frac{\pi}{11}}{2} = \frac{\pi}{11} \times \frac{1}{2} = \frac{\pi}{22}$$ 5. **Calculate the percent:** $$\text{Percent} = \frac{\pi}{22} \times 100 = \frac{100\pi}{22}$$ 6. **Simplify the fraction:** $$\frac{100\pi}{22} = \frac{50\pi}{11}$$ 7. **Approximate the value:** Using $\pi \approx 3.1416$, $$\text{Percent} \approx \frac{50 \times 3.1416}{11} = \frac{157.08}{11} \approx 14.28\%$$ **Final answer:** $\frac{\pi}{11}$ radians is approximately 14.28% of 2 radians.