Question

An aquarium pumps filtered seawater from the bay into its exhibits at a rate of 1.2×105 gallons per hour. How many gallons of seawater are pumped into the exhibits in a full day?
Write your answer in scientific notation.

Answer 1

To find out how many gallons of seawater are pumped into the exhibits in a full day, we start by calculating the number of hours in a day:

\[
24 \text{ hours/day}
\]

Next, we multiply the pumping rate by the total hours in a day:

\[
1.2 \times 10^5 \text{ gallons/hour} \times 24 \text{ hours}
\]

Calculating the multiplication:

\[
1.2 \times 24 = 28.8
\]

Now, we combine this with the scientific notation:

\[
28.8 \times 10^5
\]

To express this value in standard scientific notation, we adjust \(28.8\) so that there's only one non-zero digit to the left of the decimal by moving the decimal point one place to the left:

\[
28.8 = 2.88 \times 10^1
\]

Now we combine this with the \(10^5\):

\[
2.88 \times 10^1 \times 10^5 = 2.88 \times 10^{1+5} = 2.88 \times 10^6
\]

Thus, the number of gallons of seawater pumped into the exhibits in a full day, written in scientific notation, is:

\[
\boxed{2.88 \times 10^6}
\]