1. **State the problem:** Calculate the value of the expression $\frac{1}{0.414} + 1$. 2. **Recall the formula:** Division and addition are basic arithmetic operations. We first divide 1 by 0.414, then add 1 to the result. 3. **Calculate the division:** $$\frac{1}{0.414} \approx 2.4154589372$$ 4. **Add 1 to the result:** $$2.4154589372 + 1 = 3.4154589372$$ 5. **Final answer:** $$\boxed{3.415}$$ (rounded to three decimal places)