Rhode Island is about 116 times smaller than New Mexico.

New Mexico is approximately 314,310 sq km, while Rhode Island is approximately 2,706 sq km, making Rhode Island 0.86% the size of New Mexico. Meanwhile, the population of New Mexico is ~2.1 million people (1.0 million fewer people live in Rhode Island).
Tip: This to-scale comparison of New Mexico vs. Rhode Island uses the Mercator projection, which distorts the size of regions near the poles.