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 2.5 times 10 cubed feet and the right side labeled 3.3 times 10 cubed feet
Part A) If half of the field is used to grow crops, what is the area of the portion of the field that has crops growing? Show every step of your work.
Part B) Write the final answer in scientific notation with the correct number of significant digits, and label it with the correct units.
Part C) Explain how you chose the number of significant digits in the final answer.
To find the area of the portion of the field that has crops growing, we need to find half of the total area of the field.
Part A)
The total area of the field is given by the product of the length and width of the rectangle.
Area = length x width = (2.5 x 10^3 ft) x (3.3 x 10^3 ft)
To find half of the area, we divide the total area by 2.
Half Area = (2.5 x 10^3 ft x 3.3 x 10^3 ft) / 2
Using the laws of exponents, we can simplify the expression:
Half Area = (2.5 x 3.3) x (10^3 ft x 10^3 ft) / 2
= 8.25 x 10^6 ft^2 / 2
= 4.125 x 10^6 ft^2
Part B)
The final answer in scientific notation with the correct number of significant digits is 4.125 x 10^6 ft^2.
Part C)
I chose the number of significant digits in the final answer to match the number of significant digits given in the measurements provided (2.5 and 3.3). Since both measurements have 2 significant digits, the final answer is rounded to 3 significant digits to maintain consistency.
To find the area of the portion of the field that has crops growing, we need to find half of the total area of the field.
Part A:
Area of the field = length × width
= (2.5 × 10^3 ft) × (3.3 × 10^3 ft)
= (2.5 × 3.3) × (10^3 ft × 10^3 ft)
= 8.25 × 10^6 ft²
Half the area of the field = (8.25 × 10^6 ft²) ÷ 2
= 4.125 × 10^6 ft²
Part B:
The final answer in scientific notation with the correct number of significant digits is 4.1 × 10^6 ft².
Part C:
In the given dimensions (2.5 × 10^3 ft and 3.3 × 10^3 ft), each measurement is given to two significant digits. When multiplying these measurements, we multiply the significant digits and then use the least number of significant digits as the final answer. In this case, both measurements have two significant digits, so the final answer should have two significant digits as well. Hence, the answer is 4.1 × 10^6 ft².
Part A) To find the area of the portion of the field that has crops growing, we need to calculate half of the total area of the field.
The total area of the rectangular field can be found by multiplying the length and width of the rectangle. In this case, the length is given as 2.5 * 10^3 feet and the width is given as 3.3 * 10^3 feet.
So, the total area (A) can be calculated as:
A = length * width
A = (2.5 * 10^3) * (3.3 * 10^3)
To simplify this calculation, we can multiply the two numbers outside of the scientific notation:
A = (2.5 * 3.3) * (10^3 * 10^3)
Now, multiply the decimal numbers and add the powers of 10:
A = 8.25 * 10^6
Part B) To write the final answer in scientific notation with the correct number of significant digits and units, we first need to determine the significant digits.
The number 8.25 has three significant digits. In scientific notation, we need to express this number as a value between 1 and 10, multiplied by a power of 10. In this case, it's already in appropriate scientific notation form.
The units for the area are square feet, so the final answer would be:
8.25 * 10^6 square feet.
Part C) I chose the number of significant digits in the final answer based on the given data. Since both dimensions (length and width) were given with three significant digits, the final answer was also expressed with three significant digits to maintain consistency. Additionally, significant digits are important in calculations to maintain the precision of the result.