South Dakota is about 8 times smaller than Alaska.

Alaska is approximately 1,481,348 sq km, while South Dakota is approximately 196,540 sq km, making South Dakota 13.27% the size of Alaska. Meanwhile, the population of Alaska is ~710,231 people (103,949 more people live in South Dakota).
Tip: This to-scale comparison of Alaska vs. South Dakota uses the Mercator projection, which distorts the size of regions near the poles.