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

South Dakota is approximately 196,540 sq km, while District of Columbia is approximately 177 sq km, making District of Columbia 0.09% the size of South Dakota. Meanwhile, the population of South Dakota is ~814,180 people (212,457 fewer people live in District of Columbia).
Tip: This to-scale comparison of South Dakota vs. District of Columbia uses the Mercator projection, which distorts the size of regions near the poles.