Question

A set of four stars form the shape of a rectangle in space. The length of the rectangle is approximately 5,360,000,000 miles, while the width of the rectangle is approximately 4,050,000,000 miles. What is the approximate area of the rectangle?

Answer 1

To find the area of a rectangle, you can use the formula:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

For the rectangle described in the problem, the length is approximately 5,360,000,000 miles and the width is approximately 4,050,000,000 miles.

Plugging the numbers into the formula gives:

\[
\text{Area} = 5,360,000,000 \, \text{miles} \times 4,050,000,000 \, \text{miles}
\]

To simplify the multiplication, we can first convert the numbers into scientific notation:

- \( 5,360,000,000 \) can be written as \( 5.36 \times 10^9 \)
- \( 4,050,000,000 \) can be written as \( 4.05 \times 10^9 \)

Now, we can multiply these two numbers:

\[
\text{Area} = (5.36 \times 10^9) \times (4.05 \times 10^9)
\]

Using the properties of exponents, we can multiply the coefficients and add the exponents:

\[
\text{Area} = (5.36 \times 4.05) \times (10^9 \times 10^9)
\]

Calculating \( 5.36 \times 4.05 \):

\[
5.36 \times 4.05 \approx 21.658
\]

Calculating \( 10^9 \times 10^9 \):

\[
10^9 \times 10^9 = 10^{18}
\]

Putting it all together, we have:

\[
\text{Area} \approx 21.658 \times 10^{18} \, \text{square miles}
\]

For a more concise answer, we can express this in standard form:

\[
\text{Area} \approx 2.1658 \times 10^{19} \, \text{square miles}
\]

So the approximate area of the rectangle is:

\[
\text{Area} \approx 2.17 \times 10^{19} \, \text{square miles}
\]