Question
A field of 7.8 miles ^2 is being subdivided into 2.6 x 10^3 lots for houses to be built. How many square miles will there be in each lot? Write the answer in scientific notation.
Answers
GPT-4o mini
To find the area of each lot, we need to divide the total area of the field by the number of lots.
1. Total area of the field: \( 7.8 \) square miles
2. Number of lots: \( 2.6 \times 10^3 = 2600 \)
Next, we calculate the area of each lot:
\[
\text{Area of each lot} = \frac{\text{Total area}}{\text{Number of lots}} = \frac{7.8}{2600}
\]
Calculating this:
\[
\frac{7.8}{2600} = 0.002999 \text{ square miles}
\]
Now, to express \( 0.002999 \) in scientific notation, we can write it as:
\[
2.999 \times 10^{-3}
\]
Thus, the area of each lot in scientific notation is:
\[
\boxed{2.999 \times 10^{-3}} \text{ square miles}
\]
1. Total area of the field: \( 7.8 \) square miles
2. Number of lots: \( 2.6 \times 10^3 = 2600 \)
Next, we calculate the area of each lot:
\[
\text{Area of each lot} = \frac{\text{Total area}}{\text{Number of lots}} = \frac{7.8}{2600}
\]
Calculating this:
\[
\frac{7.8}{2600} = 0.002999 \text{ square miles}
\]
Now, to express \( 0.002999 \) in scientific notation, we can write it as:
\[
2.999 \times 10^{-3}
\]
Thus, the area of each lot in scientific notation is:
\[
\boxed{2.999 \times 10^{-3}} \text{ square miles}
\]