New Jersey is about 10 times smaller than South Dakota.

South Dakota is approximately 196,540 sq km, while New Jersey is approximately 19,211 sq km, making New Jersey 9.77% the size of South Dakota. Meanwhile, the population of South Dakota is ~814,180 people (8.0 million more people live in New Jersey).
Tip: This to-scale comparison of South Dakota vs. New Jersey uses the Mercator projection, which distorts the size of regions near the poles.