Question

A state park has two pools. The olympic size pool holds 8.12 x 10^5 gallons of water and the smaller pool holds 5.27 x 10^5 gallons of water. What is the combined capacity of the pools?

Answer 1

To find the combined capacity of the two pools, we need to add the volumes of both pools together.

The volumes are:
- Olympic size pool: \( 8.12 \times 10^5 \) gallons
- Smaller pool: \( 5.27 \times 10^5 \) gallons

We can perform the addition as follows:

\[
8.12 \times 10^5 + 5.27 \times 10^5
\]

Since both numbers are expressed in terms of \( 10^5 \), we can add the coefficients directly:

\[
(8.12 + 5.27) \times 10^5
\]

Calculating the sum of the coefficients:

\[
8.12 + 5.27 = 13.39
\]

Now, multiplying back by \( 10^5 \):

\[
13.39 \times 10^5
\]

To express the result in standard scientific notation, we can write \( 13.39 \) as \( 1.339 \times 10^1 \):

\[
13.39 \times 10^5 = 1.339 \times 10^1 \times 10^5 = 1.339 \times 10^{1 + 5} = 1.339 \times 10^6
\]

Thus, the combined capacity of the pools is:

\[
\boxed{1.339 \times 10^6} \text{ gallons}
\]