An area that is 3.2 square miles will be divided into 1.6 x 10^3 lots. How big will each lot be in scientific notation?
show work
To find the size of each lot, we divide the total area by the number of lots:
Size of each lot = Total area / Number of lots
In this case, the total area is 3.2 square miles and the number of lots is 1.6 x 10^3. Let's calculate:
Size of each lot = 3.2 square miles / (1.6 x 10^3) lots
To divide by 1.6 x 10^3, we can divide the numerator and denominator separately:
Size of each lot = (3.2 / 1.6) square miles / (10^3 / 1) lots
Simplifying the numerator and denominator:
Size of each lot = 2 square miles / (10^3) lots
The exponent in scientific notation shows that we need to move the decimal point 3 places to the right, so let's rewrite the denominator as 1000:
Size of each lot = 2 square miles / 1000 lots
Finally, let's express the answer in scientific notation:
Size of each lot = 2.0 x 10^-3 square miles/lot
To determine the size of each lot, we need to divide the area by the number of lots.
Area of the land = 3.2 square miles
Number of lots = 1.6 x 10^3
To divide the area by the number of lots, we can simply divide the numerical values and subtract the exponents:
3.2 square miles / (1.6 x 10^3) lots = (3.2 / 1.6) square miles x (10^0 / 10^3) lots
Simplifying this equation:
= 2 square miles x 10^(0-3) lots
= 2 square miles x 10^(-3) lots
Therefore, each lot will be 2 square miles in size and can be expressed in scientific notation as 2 x 10^(-3) square miles.
To find the size of each lot in scientific notation, we need to divide the given area (3.2 square miles) by the number of lots (1.6 x 10^3).
First, let's convert the area from square miles to square units. Since 1 mile = 5280 feet, we can convert the area as follows:
Area in square units = Area in square miles x (5280)^2
= 3.2 x (5280)^2
= 3.2 x 27878400
≈ 89287680 square units
Now, we divide the area in square units by the number of lots in scientific notation:
Size of each lot = Area in square units / Number of lots
= 89287680 square units / (1.6 x 10^3 lots)
To simplify the division, we need to make both the numerator and denominator have the same exponent. Let's convert 89287680 square units to scientific notation:
89287680 = 8.928768 x 10^7
Now, let's substitute it back into our equation:
Size of each lot ≈ (8.928768 x 10^7) / (1.6 x 10^3)
When dividing two scientific notation numbers, the exponents are subtracted, and the coefficients are divided. Thus:
Size of each lot ≈ (8.928768 / 1.6) x 10^(7 - 3)
= 5.58048 x 10^4
Therefore, each lot will be approximately 5.58048 x 10^4 square units in scientific notation.