A field of 3.9m * i ^ 2 is being subdivided into 1.3 * 10 ^ 3 family gardensHow many square miles will there be in each garden? Write the answer in scientific notation (1 point)
To find the area of each garden, we divide the total area of the field by the number of gardens:
Area of each garden = Area of field / Number of gardens = (3.9m * i^2) / (1.3 * 10^3)
To express the area in square miles, we need to convert meters to miles. 1 meter is approximately equal to 0.000621371 miles. So, we multiply the area in meters by this conversion factor:
Area in square miles = (3.9m * i^2) * (0.000621371 miles/meter)
Now, to write the answer in scientific notation, we need to express it in the form (a * 10^b), where a is a number between 1 and 10, and b is an integer.
Let's calculate the area in square miles:
Area in square miles = (3.9 * 0.000621371) * i^2 = 0.002423319509 * i^2
Therefore, each garden will have an area of approximately 0.002423319509 * i^2 square miles.
In scientific notation, this can be expressed as 2.423319509 × 10^-3 * i^2 square miles.
To find the area of each garden in square miles, we need to convert the given area from square meters to square miles.
1 square mile is equal to 2.59 * 10^6 square meters.
Given that the field has an area of 3.9m * i^2, we can multiply it by the conversion factor to get the area in square miles.
Therefore, the area of each garden in square miles is:
(3.9m * i^2) * (1 square mile / 2.59 * 10^6 square meters)
To simplify, we can use the fact that the imaginary unit i^2 is equal to -1:
(3.9m * (-1)) * (1 square mile / 2.59 * 10^6 square meters)
-3.9m * 1 square mile / 2.59 * 10^6 square meters
Simplifying further, we get:
-3.9m / (2.59 * 10^6) square miles
Now, we can substitute the given value of m from the question, which is 1.3 * 10^3:
-3.9 * (1.3 * 10^3) / (2.59 * 10^6) square miles
Finally, we can multiply the numbers and add the exponents to get the final answer in scientific notation:
-5.07 * 10^-3 square miles
Therefore, there will be approximately 5.07 * 10^-3 square miles in each garden.
To find the area of each family garden, we need to divide the total area of the field by the number of gardens.
The area of the field is given as 3.9m * i^2, but we need to convert it to a more common unit, such as square meters (m^2), before proceeding.
To convert the area to square meters, we need to know the conversion factor from square miles to square meters.
1 square mile is equal to approximately 2.59 * 10^6 square meters.
So, we can multiply the area of the field by the conversion factor to get the area in square meters:
3.9m * i^2 * 2.59 * 10^6 m^2/square mile
Next, we divide this total area by the number of gardens, which is 1.3 * 10^3:
(3.9m * i^2 * 2.59 * 10^6 m^2/square mile) / (1.3 * 10^3 gardens)
To simplify the expression, we combine the exponents and divide the coefficients:
(3.9 * 2.59) * (m * m^2/square mile) / (i^2 * gardens)
(3.9 * 2.59) = 10.101
(m * m^2/square mile) = m^3/square mile
(i^2 * gardens) = i^2 * gardens
So, the final expression becomes:
10.101 * (m^3/square mile) / (i^2 * gardens)
To write the answer in scientific notation, we can combine the coefficients and the units:
10.101 * (m^3/square mile) / (i^2 * gardens)
= 10.101 * (m^3/square mile) / (i^2 * 1.3 * 10^3)
≈ 7.774 * 10^(-4) * (m^3/square mile) / (i^2)
Therefore, there will be approximately 7.774 * 10^(-4) square miles in each garden.