5. 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 your work.
To find the size of each lot, we need to divide the area by the number of lots.
The area is given as 3.2 square miles.
The number of lots is given as 1.6 x 10^3.
To divide the area by the number of lots, we can write the division as follows:
(3.2 square miles) / (1.6 x 10^3 lots)
To divide the numbers, we divide the magnitudes (3.2 / 1.6) and subtract the exponents (10^3).
3.2 / 1.6 = 2
10^3 = 1000
Therefore, each lot will be (2 square miles) / (1000 lots) = 0.002 square miles.
In scientific notation, 0.002 can be written as 2 x 10^(-3).
So, each lot will be 2 x 10^(-3) square miles.
To determine the size of each lot in scientific notation, we need to divide the total area (in square miles) by the number of lots.
The area is given as 3.2 square miles, and the number of lots is 1.6 x 10^3.
First, let's divide the area by the number of lots:
Area = 3.2 sq miles
Number of lots = 1.6 x 10^3
Each lot size = Area / Number of lots
= 3.2 sq miles / (1.6 x 10^3)
To divide by a number expressed in scientific notation, we can convert the divisor to standard notation.
1.6 x 10^3 = 1.6 x 1000
Now we can perform the division:
= 3.2 sq miles / (1.6 x 1000)
= 3.2 sq miles / 1600
= 0.002 sq miles per lot
The result is 0.002 square miles per lot.
To express this in scientific notation, we need to convert it to a number between 1 and 10 multiplied by a power of 10.
0.002 can be expressed as 2 x 10^-3.
Therefore, each lot will be 2 x 10^-3 square miles in scientific notation.
To find the size of each lot in scientific notation, you need to divide the total area of 3.2 square miles by the number of lots, which is 1.6 x 10^3.
Let's break it down step-by-step:
Step 1: Convert the area from square miles to square units.
1 square mile = 27,878,400 square feet (approximately)
1 square mile = (27,878,400 square feet) * (144 square inches/square foot)
1 square mile = 4,014,489,600 square inches
Step 2: Divide the area in square inches by the number of lots.
Area per lot = (4,014,489,600 square inches) ÷ (1.6 x 10^3 lots)
Step 3: Simplify the division.
Area per lot = 4,014,489,600 square inches ÷ 1,600 lots
Step 4: Calculate the area per lot.
Area per lot = 2,508,056 square inches
Step 5: Express the area per lot in scientific notation.
Area per lot = 2.508056 x 10^6 square inches
Therefore, each lot will be approximately 2.508056 x 10^6 square inches in size.