1. **State the problem:** We need to add the numbers $5.3 \times 10^4$ and $4.7 \times 10^4$ and express the result in scientific notation. 2. **Recall the rule for adding numbers in scientific notation:** When the powers of 10 are the same, add the coefficients and keep the power of 10 unchanged. 3. **Add the coefficients:** $$5.3 + 4.7 = 10.0$$ 4. **Write the intermediate sum:** $$10.0 \times 10^4$$ 5. **Convert to proper scientific notation:** Scientific notation requires the coefficient to be between 1 and 10. $$10.0 \times 10^4 = \cancel{10.0} \times 10^4 = 1.0 \times 10 \times 10^4 = 1.0 \times 10^{1+4} = 1.0 \times 10^5$$ 6. **Final answer:** $$\boxed{1.0 \times 10^5}$$