Bot GPT 4-o mini 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:
\[ \text{Area} \approx 2.17 \times 10^{19} , \text{square miles} \]
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