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?

Responses
A 1.339 x 10^4 gallons1.339 x 10 4 gallons
B 1.339 x 10^6 gallons1.339 x 10 6 gallons
C 13.39 x 10^10 gallons13.39 x 10 10 gallons
D 1.339 x 10^10 gallons1.339 x 10 10 gallons
E 2.85 x 10^5 gallons

1 answer

To find the combined capacity of the two pools, we need to add the capacities of each pool together.

The capacities are:

  • Olympic size pool: \( 8.12 \times 10^5 \) gallons
  • Smaller pool: \( 5.27 \times 10^5 \) gallons

To add these, we can keep them in scientific notation:

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

Calculating the addition:

\[ 8.12 + 5.27 = 13.39 \]

So we have:

\[ 13.39 \times 10^5 \]

Now we need to express this in standard scientific notation, where the coefficient is between 1 and 10. We can convert \( 13.39 \times 10^5 \) to this format:

\[ 13.39 = 1.339 \times 10^1 \quad \text{(since \( 13.39 = 1.339 \times 10^1 \))} \]

This means:

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

Therefore, the combined capacity of the pools is:

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

The correct answer is:

B \( 1.339 \times 10^6 \) gallons