To find out how much larger North Dakota is compared to Washington, D.C., we need to subtract the area of Washington, D.C. from the area of North Dakota.
The areas are given as follows:
- North Dakota: \(1.83 \times 10^5\) square kilometers
- Washington, D.C.: \(1.77 \times 10^2\) square kilometers
First, we should convert the area of Washington, D.C. to have the same exponent as North Dakota for easier subtraction:
\[ 1.77 \times 10^2 = 0.0177 \times 10^5 \]
Now we can perform the subtraction:
\[ 1.83 \times 10^5 - 0.0177 \times 10^5 = (1.83 - 0.0177) \times 10^5 \]
Calculating the subtraction:
\[ 1.83 - 0.0177 = 1.8123 \]
So, we have:
\[ 1.8123 \times 10^5 \]
Now we want to express this in scientific notation. \(1.8123\) is already in proper form, so we can present the final answer as:
\[ 1.8123 \times 10^5 \text{ square kilometers} \]
Thus, the approximate area difference between North Dakota and Washington, D.C., expressed in scientific notation, is:
\[ \text{Answer: } 1.8123 \times 10^5 \text{ square kilometers} \]