Question

A certain animated movie earned
\[\$1.1 \cdot 10^9\] in revenues at the box office. The movie lasts
\[9.1\cdot10^1\] minutes.
How much revenue was earned per minute of the movie?
Write your final answer in scientific notation, and round to two decimal places.
\[\$\]

Answer 1

To find the revenue earned per minute of the movie, we need to divide the total revenue by the total duration of the movie in minutes.

Given:
- Total revenue = \( \$1.1 \cdot 10^9 \)
- Duration of the movie = \( 9.1 \cdot 10^1 \) minutes

Calculating the revenue per minute:

\[
\text{Revenue per minute} = \frac{\text{Total revenue}}{\text{Duration of the movie}} = \frac{1.1 \cdot 10^9}{9.1 \cdot 10^1}
\]

We can simplify this division step-by-step:

1. Divide the coefficients:
\[
\frac{1.1}{9.1} \approx 0.1208791
\]

2. Divide the powers of ten:
\[
\frac{10^9}{10^1} = 10^{9-1} = 10^8
\]

Combining both results, we have:
\[
\text{Revenue per minute} \approx 0.1208791 \cdot 10^8
\]

To express this in proper scientific notation, we convert \(0.1208791\) to \(1.208791\) and decrease the power of ten by 1:

\[
0.1208791 \cdot 10^8 = 1.208791 \cdot 10^7
\]

Now we round \(1.208791\) to two decimal places:
\[
1.21 \cdot 10^7
\]

Thus, the revenue earned per minute of the movie, expressed in scientific notation and rounded to two decimal places, is:

\[
\boxed{\$1.21 \cdot 10^7}
\]