The approximate areas of North Dakota and Washington, D.C. are listed below:

North Dakota: 1, point, 8, 3, times, 10, to the power 51.83×10
5
square kilometers
Washington, D.C.: 1, point, 7, 7, times, 10, squared1.77×10
2
square kilometers
How much larger is North Dakota? Express your answer using scientific notation.

Answer
Attempt 1 out of 2

Answer:
times, 10×10
square kilometers

1 answer

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:

\[ \text{Answer: } 1.8123 \times 10^5 \text{ square kilometers} \]