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.

Question

GPT-4o mini · Accepted Answer

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

Weight of water per gallon: 8.3 lb/gallon
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.