A field of 3.9 mi2

is being subdivided into 1.3×103
family gardens. How many square miles will there be in each garden? Write the answer in scientific notation.(1 point)
×
miles squared

1 answer

To find the area of each garden, you can divide the total area of the field by the number of family gardens.

  1. Total area of the field:
    \( 3.9 , \text{mi}^2 \)

  2. Number of family gardens:
    \( 1.3 \times 10^3 \)

Now, calculate the area of each garden:

\[ \text{Area of each garden} = \frac{\text{Total area}}{\text{Number of gardens}} = \frac{3.9 , \text{mi}^2}{1.3 \times 10^3} \]

First, convert \( 3.9 \) into scientific notation \( 3.9 = 3.9 \times 10^0 \):

\[ \frac{3.9 \times 10^0}{1.3 \times 10^3} = \frac{3.9}{1.3} \times \frac{10^0}{10^3} \]

Now, calculate \( \frac{3.9}{1.3} \):

\[ \frac{3.9}{1.3} \approx 3.0 \quad (\text{since } 3.9 \div 1.3 \approx 3.0) \]

This can be expressed in scientific notation: \[ 3.0 = 3.0 \times 10^0 \]

Now, calculate \( \frac{10^0}{10^3} = 10^{-3} \):

So now we combine:

\[ \frac{3.9 , \text{mi}^2}{1.3 \times 10^3} \approx 3.0 \times 10^{-3} , \text{mi}^2 \]

Thus, the area of each garden is approximately:

\[ \boxed{3.0 \times 10^{-3}} , \text{mi}^2 \]