1. The problem is to convert 1000 degrees to radians. 2. The formula to convert degrees to radians is $\text{radians} = \text{degrees} \times \frac{\pi}{180}$. 3. This formula works because $180$ degrees equals $\pi$ radians. 4. Substitute 1000 degrees into the formula: $$1000 \times \frac{\pi}{180}$$ 5. Simplify the fraction: $$\frac{1000}{180} = \frac{100}{18} = \frac{50}{9}$$ 6. So the radians measure is: $$\frac{50}{9} \pi$$ 7. Therefore, 1000 degrees equals $\frac{50}{9} \pi$ radians, which is approximately $17.45$ radians. This step-by-step explanation shows how to use the conversion formula and simplify the fraction to get the final answer.