To find the area of each garden, you can divide the total area of the field by the number of family gardens.
-
Total area of the field:
\( 3.9 , \text{mi}^2 \) -
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:
\[ \boxed{3.0 \times 10^{-3}} , \text{mi}^2 \]