The construct of science identity has been gaining attention across various domains in the educational arena. To date, however, no studies have used a person-centered quantitative approach within science identity research that is based upon traditional identity theory. Hence, there is an absence of a theoretical underpinning of the number of science identity classes that might be derived from using person-centered techniques or descriptive dialogues of such classes. Due to this gap in the research and the potentially significant impact of science identity on students' pursuit of STEM studies and subsequent careers, our project team tested the Science Identity Scale rooted in traditional identity theory with a group of rural high school students. Using latent class analysis, an optimal 4-class science identity solution emerged that reflected the four traditional identity statuses -- Achieved, Foreclosed, Moratorium, and Diffused. These classifications predicted student science career interest but also suggested the existence of social inequalities for low socioeconomic students, Latinxs, and African Americans. More study is needed to investigate classification stability over time and to identify factors that contribute to existing social inequalities, thereby providing insight into the effective cultivation of students' science identities and culminating in greater STEM persistence with less inequality.