South Dakota is about 1,110 times bigger than District of Columbia.

District of Columbia is approximately 177 sq km, while South Dakota is approximately 196,540 sq km, making South Dakota 110,940% larger than District of Columbia. Meanwhile, the population of District of Columbia is ~601,723 people (212,457 more people live in South Dakota).
Tip: This to-scale comparison of District of Columbia vs. South Dakota uses the Mercator projection, which distorts the size of regions near the poles.