To solve the problem, we'll first calculate the area of the rectangular field and then find the area used for growing corn.
Part A: Area of the Field
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{width} \]
From the problem statement, we have:
- Length = \( 2.7 \times 10^3 \) feet
- Width = \( 3.5 \times 10^3 \) feet
Now, we can calculate the area:
\[ A = (2.7 \times 10^3) \times (3.5 \times 10^3) \]
Using the property of multiplying numbers in scientific notation, we can multiply the coefficients (the numbers) and then add the exponents of 10.
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Multiply the coefficients: \[ 2.7 \times 3.5 = 9.45 \]
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Add the exponents of 10: \[ 10^3 \times 10^3 = 10^{3+3} = 10^6 \]
Combining these results, we have:
\[ A = 9.45 \times 10^6 \]
Since we need to express our answer in scientific notation, we check if the coefficient (9.45) is in the correct range (between 1 and 10). It is.
Thus, the area of the field is: \[ \boxed{9.45 \times 10^6} \text{ square feet} \]
Part B: Area Used to Grow Corn
If half of the field is used to grow corn, we take half of the total area calculated in Part A:
\[ \text{Area for Corn} = \frac{A}{2} = \frac{9.45 \times 10^6}{2} \]
Calculating this:
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Divide the coefficient by 2: \[ \frac{9.45}{2} = 4.725 \]
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The exponent remains the same: \[ 10^6 \]
Now we express the area used for corn in scientific notation. Since \( 4.725 \) is also within the range (1 to 10), we can express it as:
\[ \text{Area for Corn} = 4.725 \times 10^6 \]
Thus, the area used to grow corn is: \[ \boxed{4.725 \times 10^6} \text{ square feet} \]