1. **Stating the problem:** Divide the decimal number 3.5 by the fraction $\frac{3}{8}$. 2. **Formula and rules:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$3.5 \div \frac{3}{8} = 3.5 \times \frac{8}{3}$$ 3. **Convert decimal to fraction:** $$3.5 = \frac{7}{2}$$ 4. **Rewrite the expression:** $$\frac{7}{2} \times \frac{8}{3}$$ 5. **Multiply numerators and denominators:** $$\frac{7 \times 8}{2 \times 3} = \frac{56}{6}$$ 6. **Simplify the fraction:** $$\frac{56}{6} = \frac{\cancel{56}^{28}}{\cancel{6}^{3}} = \frac{28}{3}$$ 7. **Convert to mixed number or decimal:** $$\frac{28}{3} = 9 \frac{1}{3} \approx 9.3333$$ **Final answer:** $$3.5 \div \frac{3}{8} = \frac{28}{3} = 9 \frac{1}{3} \approx 9.3333$$