Question

A large community farm has a total area of 2.5 × 10⁴ acres. The farm is being subdivided into 1.3 × 10³ family gardens.

Approximately how many acres will each family garden occupy? Express your answer in scientific notation.

(1 point)
Responses

1.9×100
1 point 9 times 10 to the 0 power

1.9×102
1 point 9 times 10 squared

1.9×101
1 point 9 times 10 to the 1th power

1.9×10−1

Answer 1

To find out how many acres each family garden will occupy, we need to divide the total area of the farm by the number of family gardens.

The total area of the farm is \( 2.5 \times 10^4 \) acres, and the number of family gardens is \( 1.3 \times 10^3 \).

We perform the division as follows:

\[
\text{Area per garden} = \frac{2.5 \times 10^4}{1.3 \times 10^3}
\]

To divide the numbers in scientific notation, we divide the coefficients and subtract the exponents:

\[
\text{Area per garden} = \frac{2.5}{1.3} \times 10^{4-3}
\]

Calculating \( \frac{2.5}{1.3} \):

\[
\frac{2.5}{1.3} \approx 1.9231
\]

Now, simplifying:

\[
\text{Area per garden} \approx 1.9231 \times 10^1
\]

Rounding \( 1.9231 \) to one decimal place gives \( 1.9 \).

So we have:

\[
\text{Area per garden} \approx 1.9 \times 10^1
\]

Thus, the approximate number of acres each family garden will occupy is:

\[
\boxed{1.9 \times 10^1}
\]