Question

The approximate areas of Alabama and Rhode Island are listed below:
Alabama: 1, point, 3, 6, times, 10, to the power 51.36×10
5
square kilometers
Rhode Island: 4, times, 10, cubed4×10
3
square kilometers
How many times larger is Alabama than Rhode Island? Write your answer in standard notation, rounding to the nearest tenth.

Answer 1

To find out how many times larger Alabama is than Rhode Island, we need to divide the area of Alabama by the area of Rhode Island.

1. **Areas in scientific notation**:
- Alabama: \( 1.36 \times 10^5 \) square kilometers
- Rhode Island: \( 4 \times 10^3 \) square kilometers

2. **Division of the areas**:
\[
\text{Ratio} = \frac{\text{Area of Alabama}}{\text{Area of Rhode Island}} = \frac{1.36 \times 10^5}{4 \times 10^3}
\]

3. **Calculate the numerical part**:
\[
\frac{1.36}{4} = 0.34
\]

4. **Calculate the power of ten**:
\[
\frac{10^5}{10^3} = 10^{(5 - 3)} = 10^2
\]

5. **Combine the results**:
\[
\text{Ratio} = 0.34 \times 10^2 = 34
\]

Thus, Alabama is approximately 34 times larger than Rhode Island.

In standard notation, rounded to the nearest tenth, the answer is:

\[
\boxed{34.0}
\]