1. **State the problem:** Simplify the expression $$\frac{3 \times 10^{-2}}{8 \times 10^{-1}}$$. 2. **Recall the rule for division of powers of 10:** When dividing terms with the same base, subtract the exponents: $$\frac{10^a}{10^b} = 10^{a-b}$$. 3. **Rewrite the expression by separating constants and powers of 10:** $$\frac{3}{8} \times \frac{10^{-2}}{10^{-1}}$$ 4. **Apply the exponent subtraction rule:** $$\frac{3}{8} \times 10^{-2 - (-1)} = \frac{3}{8} \times 10^{-2 + 1} = \frac{3}{8} \times 10^{-1}$$ 5. **Calculate the fraction:** $$\frac{3}{8} = 0.375$$ 6. **Combine the results:** $$0.375 \times 10^{-1} = 0.375 \times 0.1 = 0.0375$$ **Final answer:** $$\boxed{0.0375}$$