1. **State the problem:** A pole is 10 \frac{1}{5} meters tall and is cut into 12 equal pieces. We need to find the length of each piece. 2. **Convert mixed number to improper fraction:** $$10 \frac{1}{5} = \frac{10 \times 5 + 1}{5} = \frac{50 + 1}{5} = \frac{51}{5}$$ 3. **Formula used:** To find the length of each piece when a total length is divided into equal parts, use: $$\text{Length of each piece} = \frac{\text{Total length}}{\text{Number of pieces}}$$ 4. **Apply the formula:** $$\text{Length of each piece} = \frac{\frac{51}{5}}{12} = \frac{51}{5} \times \frac{1}{12} = \frac{51}{60}$$ 5. **Simplify the fraction:** $$\frac{51}{60} = \frac{17}{20}$$ 6. **Convert to decimal (optional):** $$\frac{17}{20} = 0.85$$ **Answer:** Each piece is \boxed{\frac{17}{20}} meters or 0.85 meters long.