1. **State the problem:** We want to find the relative error when approximating the expression $5x^2 - 1$ using 4-digit chopping for $x = 11110.3338$. 2. **Recall the formula for relative error:** $$\text{Relative error} = \frac{|\text{Exact value} - \text{Approximate value}|}{|\text{Exact value}|}$$ 3. **Calculate the exact value:** $$x = 11110.3338$$ $$5x^2 - 1 = 5 \times (11110.3338)^2 - 1$$ First, calculate $x^2$: $$11110.3338^2 = 123456790.1115 \text{ (approx)}$$ Then multiply by 5 and subtract 1: $$5 \times 123456790.1115 - 1 = 617283945.5575$$ 4. **Calculate the approximate value using 4-digit chopping:** Chop $x$ to 4 digits: $$x_{chopped} = 11110$$ Calculate $x_{chopped}^2$: $$11110^2 = 123432100$$ Calculate approximate value: $$5 \times 123432100 - 1 = 617160499$$ 5. **Calculate the relative error:** $$\text{Relative error} = \frac{|617283945.5575 - 617160499|}{|617283945.5575|} = \frac{123446.5575}{617283945.5575} \approx 0.0002$$ 6. **Interpretation:** The relative error is approximately $0.0002$, which means the 4-digit chopping approximation introduces a small error of about 0.02%.