Math 8A Unit 4 Study Guide
14. A field of 7.8m * i ^ 2 is being subdivided into 2.6 * 10 ^ 3 lots for houses to be built. How many square miles will there be in each lot? Write the answer in scientific notation.
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To find the area of each lot in square miles, we need to convert the given area of the field from square meters to square miles.
First, we convert the square meters to square kilometers by dividing by 10^6 (since 1 square kilometer = 1,000,000 square meters):
7.8 m * (1 km / 1000 m)^2 = 7.8 * 10^-6 km^2
Next, we convert square kilometers to square miles by multiplying by 0.386102 (since 1 square mile = 2.58999 square kilometers):
7.8 * 10^-6 km^2 * 0.386102 = 3.0105356 * 10^-6 sq mi
Finally, to find the area of each lot, we divide the total area by the number of lots:
(3.0105356 * 10^-6 sq mi) / (2.6 * 10^3 lots) = 1.1582807 * 10^-9 sq mi
Therefore, there will be approximately 1.16 * 10^-9 square miles in each lot.
To find the number of square miles in each lot, we need to convert the given area from meters squared to miles squared.
1 mile is approximately equal to 1609.34 meters.
To convert from meters squared to miles squared, we need to divide the given area in meters squared by the square of the conversion factor (1609.34)^2.
Let's calculate the number of square miles in each lot.
Area in meters squared = 7.8 m * i^2
Conversion factor: 1 mile ≈ 1609.34 meters
1 mile squared ≈ (1609.34)^2 meters squared
Area in miles squared = (7.8 m * i^2) / (1609.34^2)
Calculating the result:
Area in miles squared = 7.8 / (1609.34^2) m^2
Area in miles squared = 7.8 / 2.58806 * 10^6 m^2
We divide 7.8 by 2.58806 * 10^6 and express the answer in scientific notation.
The number of square miles in each lot is 3.009 * 10^-7 square miles.
To find the number of square miles in each lot, we need to convert the given area from square meters to square miles.
1 square mile is equal to 2590000 square meters.
First, we'll convert the given area of the field from square meters to square miles:
7.8m * i^2 * (1 square mile / 2590000 square meters)
To simplify this expression:
7.8 / 2590000 square miles
Dividing the numerator by the denominator:
7.8 / 2590000 = 3 * 10^-6 square miles
This gives us the area of the field in square miles. Next, we'll divide this area by the number of lots to find the area of each lot.
2.6 * 10^3 * (3 * 10^-6 square miles / lot)
Multiplying the numerator and denominator:
2.6 * 3 * 10^-3 square miles
Multiplying the numbers:
7.8 * 10^-3 square miles
The answer in scientific notation is 7.8 * 10^-3 square miles.