The water park currently uses \( 8.8 \times 10^5 \) gallons of water. They plan to add a ride that will use an additional \( 51,000 \) gallons of water.
First, we need to express \( 51,000 \) in scientific notation:
\[ 51,000 = 5.1 \times 10^4 \]
Now, we want to add \( 8.8 \times 10^5 \) and \( 5.1 \times 10^4 \). To do that, we need to express both numbers with the same exponent. We can express \( 5.1 \times 10^4 \) with \( 10^5 \) as the base:
\[ 5.1 \times 10^4 = 0.051 \times 10^5 \]
Now we can add:
\[ 8.8 \times 10^5 + 0.051 \times 10^5 = (8.8 + 0.051) \times 10^5 = 8.851 \times 10^5 \]
So the total amount of water used in the park after the new ride is installed is:
\[ \boxed{8.851 \times 10^5} \text{ gallons} \]