1. **State the problem:** Calculate $2.6 \cos 12^\circ$ and round the result to 2 decimal places. 2. **Recall the formula:** The cosine function for an angle $\theta$ in degrees is $\cos \theta$. 3. **Calculate the cosine:** Using a calculator or cosine table, find $\cos 12^\circ \approx 0.9781$. 4. **Multiply:** Compute $2.6 \times 0.9781 = 2.54206$. 5. **Round the result:** Rounded to 2 decimal places, $2.54206 \approx 2.54$. **Final answer:** $2.54$