1. **State the problem:** We want to find how many pieces of paper, each with thickness $8.1 \times 10^{-5}$ meters, are needed to make a stack 2 meters high. 2. **Formula:** The total height of the stack is the number of pieces times the thickness of one piece. $$ \text{Number of pieces} = \frac{\text{Total height}}{\text{Thickness of one piece}} $$ 3. **Substitute the values:** $$ \text{Number of pieces} = \frac{2}{8.1 \times 10^{-5}} $$ 4. **Calculate:** $$ \text{Number of pieces} = \frac{2}{8.1 \times 10^{-5}} = \frac{2}{0.000081} $$ 5. **Simplify:** $$ \text{Number of pieces} = 24691.3580247... $$ 6. **Interpretation:** Approximately 24691 pieces of paper are needed to make a 2-meter high stack. **Final answer:** $$ \boxed{24691} $$ pieces of paper.