Question

A farmer is planning to use the land in a rectangular field.
Rectangle with a side length of 3.5 * 10 raised to the third power ft
And width of 2.7 * 10 raised to the third power
Part A what is the area of the field?
Write your answer in scientific notation band 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 answer in scientific notation and show or explain your mathematical process

Answer 1

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:

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

2. 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.