Question

A farmer is planning how to use the land in a rectangular field. The rectangle shown represents the field.

a rectangle with the bottom labeled 2.7 times 10 cubed feet and the right side labeled 3.5 times 10 cubed feet




Part A: What is the area of the field?

Write your final answer in scientific notation and show or explain your mathematical process.



Part B: Half of the field is used to grow corn. What is the area of that section?

Write your final answer in scientific notation and show or explain your mathematical process.

Answer 1

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.

1. **Multiply the coefficients:**
\[
2.7 \times 3.5 = 9.45
\]

2. **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:

1. **Divide the coefficient by 2:**
\[
\frac{9.45}{2} = 4.725
\]

2. 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:
\[
\boxed{4.725 \times 10^6} \text{ square feet}
\]