1. **State the problem:** We want to approximate the value of the function $$f(x) = x^3 - 3x^2 + 4x + 0.21$$ at $$x = 2.15$$ using nested arithmetic and 3-digit rounding. 2. **Rewrite the function using nested form:** $$f(x) = x(x(x - 3) + 4) + 0.21$$ This form reduces the number of operations and helps with rounding at each step. 3. **Evaluate step-by-step with 3-digit rounding:** - Calculate $$x - 3 = 2.15 - 3 = -0.85$$ (already 3 digits) - Multiply $$x(x - 3) = 2.15 \times (-0.85) = -1.8275 \approx -1.83$$ (rounded to 3 digits) - Add 4: $$-1.83 + 4 = 2.17$$ (3 digits) - Multiply by $$x$$: $$2.15 \times 2.17 = 4.6655 \approx 4.67$$ (3 digits) - Add 0.21: $$4.67 + 0.21 = 4.88$$ (3 digits) 4. **Interpretation:** The approximate value of the function at $$x=2.15$$ using nested arithmetic and 3-digit rounding is $$\boxed{4.88}$$. 5. **Summary:** Nested arithmetic helps simplify calculations and control rounding errors by performing operations stepwise and rounding at each step.