The areas of both Kentucky and Rhode Island are approximately \(4 \times 10^3\) square kilometers.
To find how many times larger Kentucky is than Rhode Island, you can divide the area of Kentucky by the area of Rhode Island:
\[ \text{Size Ratio} = \frac{\text{Area of Kentucky}}{\text{Area of Rhode Island}} = \frac{4 \times 10^3}{4 \times 10^3} = 1 \]
Thus, Kentucky is 1 time larger than Rhode Island.
In standard notation, rounded to the nearest tenth, the answer is:
\[ \boxed{1.0} \]
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