1. **State the problem:** We need to divide $4.05 \times 10^{-1}$ by $1.5 \times 10^{-1}$. 2. **Write the division as a fraction:** $$\frac{4.05 \times 10^{-1}}{1.5 \times 10^{-1}}$$ 3. **Use the property of exponents:** When dividing powers of 10 with the same base, subtract the exponents: $$= \frac{4.05}{1.5} \times 10^{-1 - (-1)} = \frac{4.05}{1.5} \times 10^{0}$$ 4. **Simplify the exponent:** $$10^{0} = 1$$ 5. **Divide the coefficients:** $$\frac{4.05}{1.5} = 2.7$$ 6. **Multiply the results:** $$2.7 \times 1 = 2.7$$ **Final answer:** $$2.7$$