1. **State the problem:** Calculate the sum of $10.97 \times 10^3$ and $20.88 \times 10^3$. 2. **Formula and rules:** When adding numbers in scientific notation with the same power of 10, add the coefficients and keep the power of 10 the same. 3. **Intermediate work:** $$10.97 \times 10^3 + 20.88 \times 10^3 = (10.97 + 20.88) \times 10^3$$ $$= 31.85 \times 10^3$$ 4. **Simplify the result:** $$31.85 \times 10^3 = 3.185 \times 10^4$$ 5. **Explanation:** We added the coefficients 10.97 and 20.88 to get 31.85, then expressed the result in proper scientific notation by adjusting the coefficient to be between 1 and 10. **Final answer:** $$3.185 \times 10^4$$