To find how much larger Rhode Island is compared to Washington, D.C., we need to subtract the area of Washington, D.C. from the area of Rhode Island.
Given:
- Area of Rhode Island = \( 4 \times 10^3 \) square kilometers
- Area of Washington, D.C. = \( 1.77 \times 10^2 \) square kilometers
First, we need to express both areas in the same power of 10 for ease of subtraction. We can express \( 1.77 \times 10^2 \) in terms of \( 10^3 \):
\[ 1.77 \times 10^2 = 0.177 \times 10^3 \]
Now we can perform the subtraction:
\[ \text{Area of Rhode Island} - \text{Area of Washington, D.C.} = (4 \times 10^3) - (0.177 \times 10^3) \]
Combining the coefficients:
\[ = (4 - 0.177) \times 10^3 = 3.823 \times 10^3 \]
Thus, the area of Rhode Island is approximately \( 3.823 \times 10^3 \) square kilometers larger than the area of Washington, D.C.
Therefore, the final answer is:
\[ \boxed{3.823 \times 10^3} \]