To find the area of the rectangular field and the area used to grow corn, we can follow these steps:
Part A: Finding the Area of the Field
The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{width} \]
Given:
- Length = \( 3.5 \times 10^3 \) ft
- Width = \( 2.7 \times 10^3 \) ft
We can substitute the length and width into the formula:
\[ A = (3.5 \times 10^3) \times (2.7 \times 10^3) \]
Using the properties of exponents and multiplication:
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Multiply the coefficients: \[ 3.5 \times 2.7 = 9.45 \]
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Add the exponents: \[ 10^3 \times 10^3 = 10^{3+3} = 10^6 \]
Now combine these results:
\[ A = 9.45 \times 10^6 \]
Since scientific notation typically uses one non-zero digit before the decimal, we need to express \( 9.45 \) in this format:
\[ 9.45 = 9.45 \times 10^0 \implies 9.45 \text{ is already in scientific notation.} \]
Thus, the area of the field is:
\[ \text{Area} = 9.45 \times 10^6 \text{ square feet}. \]
Part B: Finding the Area Used to Grow Corn
Since half of the field is used to grow corn, we can simply take half of the total area calculated in Part A:
\[ \text{Area used for corn} = \frac{1}{2} \times \text{Area} \] \[ = \frac{1}{2} \times 9.45 \times 10^6 \]
Calculating this gives:
\[ \text{Area used for corn} = 4.725 \times 10^6 \]
Again, we should express this in proper scientific notation. The number \( 4.725 \) is already in the correct format.
Thus, the area used to grow corn is:
\[ \text{Area used for corn} = 4.725 \times 10^6 \text{ square feet}. \]
Summary:
- Part A: The area of the field is \( 9.45 \times 10^6 \) square feet.
- Part B: The area used to grow corn is \( 4.725 \times 10^6 \) square feet.