1. **State the problem:** Calculate the value of $\frac{3.0 \times 10^8}{2.7}$.\n\n2. **Formula and explanation:** This is a simple division problem where we divide $3.0 \times 10^8$ by $2.7$.\n\n3. **Perform the division:**\n$$\frac{3.0 \times 10^8}{2.7} = \frac{3.0}{2.7} \times 10^8$$\n\n4. **Simplify the fraction:**\n$$\frac{3.0}{2.7} = 1.111\ldots$$\n\n5. **Multiply by $10^8$:**\n$$1.111\ldots \times 10^8 = 1.11 \times 10^8$$ (rounded to three significant figures)\n\n**Final answer:**\n$$\boxed{1.11 \times 10^8}$$