1. The problem is to calculate the value of $r_1^*$ given by the expression $r_1^* = 4.640 \times 0.083 + 0.0000020 \times 5,585,000 \times \sqrt{0.083}$. 2. First, multiply $4.640$ by $0.083$: $$4.640 \times 0.083 = 0.38512$$ 3. Next, calculate the square root of $0.083$: $$\sqrt{0.083} \approx 0.2880$$ 4. Then multiply $0.0000020$ by $5,585,000$: $$0.0000020 \times 5,585,000 = 11.17$$ 5. Now multiply the result by $\sqrt{0.083}$: $$11.17 \times 0.2880 = 3.215$$ 6. Finally, add the two parts together: $$0.38512 + 3.215 = 3.60012$$ 7. Therefore, the value of $r_1^*$ is approximately $3.600$.