1. **Problem:** Given $34^2 = 1156$, find the value of $\frac{(0.34)^2}{10^2}$. 2. **Formula and rules:** We know that $0.34 = \frac{34}{100}$ and $10^2 = 100$. So, $$\frac{(0.34)^2}{10^2} = \frac{\left(\frac{34}{100}\right)^2}{100} = \frac{\frac{34^2}{10000}}{100} = \frac{1156/10000}{100}.$$ 3. **Intermediate work:** Simplify the expression step-by-step: $$\frac{1156}{10000} \div 100 = \frac{1156}{10000} \times \frac{1}{100} = \frac{1156}{1000000} = 0.001156.$$ 4. **Explanation:** Squaring $0.34$ is the same as squaring $\frac{34}{100}$, which gives $\frac{1156}{10000}$. Dividing by $10^2 = 100$ further divides the result by 100, leading to $\frac{1156}{1000000}$. This equals $0.001156$. 5. **Answer:** The correct choice is **C) 0.001156**.