A water park has pools, slides, and rides that, in total, make use of 2, point, 1, times, 10, to the power 7

Question

gallons of water. They plan to add a ride that would make use of an additional 680, comma, 000680,000 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.

Answer 1

To express the total gallons of water used in the water park after adding the new ride, we will first express both quantities in scientific notation.

1. The current amount of water used in the park is \( 2.1 \times 10^7 \) gallons.

2. The additional water used by the new ride is \( 680,000 \) gallons. To express this in scientific notation:

   \[ 680,000 = 6.8 \times 10^5 \]

Now, we need to add \( 2.1 \times 10^7 \) and \( 6.8 \times 10^5 \). Since these numbers are in different orders of magnitude, we need to adjust them to have the same exponent for easier addition:

Convert \( 6.8 \times 10^5 \) to the same order of magnitude as \( 2.1 \times 10^7 \):

\[ 6.8 \times 10^5 = 0.068 \times 10^7 \]

Now we can add:

\[ 2.1 \times 10^7 + 0.068 \times 10^7 = (2.1 + 0.068) \times 10^7 = 2.168 \times 10^7 \]

Thus, the total gallons of water used in the park after installing the new ride is:

\[ \boxed{2.168 \times 10^7} \]