A water park has pools, slides, and rides that, in total, make use of 3.1 x 10^7 gallons of water. They plan to add a ride that would make use of an additional 2.9 x 10^3 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 find the total gallons of water made use of in the park after the new ride is installed, you need to add the current amount of water (3.1 x 10^7 gallons) to the additional amount of water for the new ride (2.9 x 10^3 gallons).

First, we should express these two amounts in a comparable form. Notice that \(10^3\) (which is 1000) is significantly smaller than \(10^7\) (which is 10,000,000). To add these two amounts, we should convert \(2.9 x 10^3\) to a form that has the same exponent as \(3.1 x 10^7\).

We can write \(2.9 x 10^3\) as: \[ 2.9 x 10^3 = 0.000029 x 10^7 \]

Now we can add: \[ 3.1 x 10^7 + 0.000029 x 10^7 = (3.1 + 0.000029) x 10^7 \]

Now, compute the sum: \[ 3.1 + 0.000029 \approx 3.100029 \]

So, we have: \[ 3.100029 x 10^7 \]

Since we typically express numbers in scientific notation with one non-zero digit to the left of the decimal point, we can write this as: \[ 3.100029 x 10^7 \approx 3.1 x 10^7 \text{ (keeping it in same significant figures)} \]

However, if we wish to give an even more precise answer, we can keep it as: \[ 3.10003 x 10^7 \]

In summary, after installing the new ride, the total gallons of water made use of in the park would be represented as: \[ \boxed{3.1 x 10^7 \text{ gallons}} \text{ or more precisely } \boxed{3.10003 x 10^7 \text{ gallons}}. \]