1. **State the problem:** Find the decimal approximation of $\cot 236^\circ 48'$. 2. **Convert the angle to decimal degrees:** $$236^\circ 48' = 236 + \frac{48}{60} = 236 + 0.8 = 236.8^\circ$$ 3. **Use the cotangent identity:** $$\cot \theta = \frac{1}{\tan \theta}$$ 4. **Calculate $\tan 236.8^\circ$ using a calculator:** $$\tan 236.8^\circ \approx 0.90040404$$ 5. **Calculate $\cot 236.8^\circ$:** $$\cot 236.8^\circ = \frac{1}{\tan 236.8^\circ} \approx \frac{1}{0.90040404}$$ 6. **Simplify the fraction:** $$\cot 236.8^\circ \approx 1.11073744$$ 7. **Final answer:** $$\cot 236^\circ 48' \approx 1.11073744$$