Question

A gallon of water weighs about 8.3 lb. An Olympic-sized swimming pool holds 6.6×105 gallons. What is the approximate weight of the water in an Olympic-sized swimming pool? Write the answer in scientific notation.(1 point) Responses 54.78×105 lb. 54 point 7 8 times 10 to the 5th power lb. 5.478×106 lb. 5 point 4 7 8 times 10 to the 6th power lb. 54.78×106 lb. 54 point 7 8 times 10 to the 6th power lb. 5.478×105 lb.

Answer 1

To calculate the weight of the water in an Olympic-sized swimming pool, we can follow these steps:

1. **Weight of water per gallon**: 8.3 lb/gallon
2. **Volume of an Olympic-sized swimming pool**: \(6.6 \times 10^5\) gallons

Now, we can multiply the weight of water per gallon by the total number of gallons:

\[
\text{Total weight} = 8.3 \, \text{lb/gallon} \times 6.6 \times 10^5 \, \text{gallons}
\]

Calculating this gives:

\[
\text{Total weight} = 8.3 \times 6.6 \times 10^5
\]

Now, calculate \(8.3 \times 6.6\):

\[
8.3 \times 6.6 = 54.78
\]

Therefore, the total weight is:

\[
54.78 \times 10^5 \, \text{lb}
\]

To express this in proper scientific notation, we should move the decimal one place to the left, which will increase the exponent by 1:

\[
54.78 \times 10^5 = 5.478 \times 10^6 \, \text{lb}
\]

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

\[
5.478 \times 10^6 \, \text{lb}
\]

The correct response from your options is:

**5.478×10^6 lb.**