To find the total surface area of Earth's water, we need to add the surface area of saltwater and freshwater:
- Surface area of saltwater: \( 352,000,000 , \text{km}^2 \) or \( 3.52 \times 10^8 , \text{km}^2 \)
- Surface area of freshwater: \( 9,000,000 , \text{km}^2 \) or \( 9 \times 10^6 , \text{km}^2 \)
Now we add these two:
\[ 3.52 \times 10^8 , \text{km}^2 + 9 \times 10^6 , \text{km}^2 \]
To add these, we can write \( 9 \times 10^6 \) in the same power of ten as \( 3.52 \times 10^8 \):
\[ 9 \times 10^6 = 0.009 \times 10^8 , \text{km}^2 \]
Now we can add:
\[ 3.52 \times 10^8 , \text{km}^2 + 0.009 \times 10^8 , \text{km}^2 = (3.52 + 0.009) \times 10^8 , \text{km}^2 = 3.529 \times 10^8 , \text{km}^2 \]
Thus, the total surface area of Earth's water is approximately:
\[ \boxed{3.529 \times 10^8} , \text{km}^2 \]