A gallon of water weighs about 8.3 pounds. An Olympic-sized swimming pool holds 6.6×10^5 gallons. What is the approximate weight of water in an Olympic-sized swimming pool. Write the answer in scientific notation.

Question

A. 54.78×10^6 pounds
B. 5.478×10^5 pounds
C. 54.78×10^5 pounds
D. 5.478×10^6 pounds

Answer 1

To find the weight of water in an Olympic-sized swimming pool, we can use the following information:

• The weight of one gallon of water is approximately 8.3 pounds.
• An Olympic-sized swimming pool holds about $6.6\times {10}^5$ gallons.

Now, we can calculate the total weight of the water in the swimming pool:

$$\text{Weight of water}=\text{Number of gallons}\times \text{Weight per gallon}$$

Substituting the values:

$$\text{Weight of water}=(6.6\times {10}^5\text{ gallons})\times (8.3\text{ pounds/gallon})$$

Calculating this:

$$\text{Weight of water}=6.6\times 8.3\times {10}^5$$

First, calculate $6.6\times 8.3$:

$$6.6\times 8.3=54.78$$

Now, including the power of 10:

$$\text{Weight of water}=54.78\times {10}^5\text{ pounds}$$

To write this in proper scientific notation, we can express $54.78$ as $5.478\times {10}^1$ so:

$$54.78\times {10}^5=5.478\times {10}^1\times {10}^5=5.478\times {10}^6$$

Thus, the approximate weight of water in an Olympic-sized swimming pool is:

$$\text{Weight of water}\approx 5.478\times {10}^6\text{ pounds}$$

The correct answer is:

D. 5.478×10^6 pounds