To find the total gallons of water used by the water park after adding the new ride, you need to add the additional water usage to the current water usage.
- The current water usage is \( 8.3 \times 10^6 \) gallons.
- The additional water usage is 380,000 gallons, which can be expressed in scientific notation as \( 3.8 \times 10^5 \) gallons.
Now, we need to add these two numbers together:
\[ 8.3 \times 10^6 + 3.8 \times 10^5 \]
Since the exponents are different, we need to convert \( 3.8 \times 10^5 \) to the same exponent as \( 8.3 \times 10^6 \):
\[ 3.8 \times 10^5 = 0.38 \times 10^6 \]
Now we can add:
\[ 8.3 \times 10^6 + 0.38 \times 10^6 = (8.3 + 0.38) \times 10^6 = 8.68 \times 10^6 \]
Thus, the total gallons of water used in the park after the new ride is installed is:
\[ \boxed{8.68 \times 10^6} \] gallons.