Our goal in this article is to organise an epistemological matrix for the concept of rational number that contemplates its different meanings. Aiming at understanding the various ways to signify the rational numbers and based on the theoretical-methodological approach of conceptual profiles, we produce and analyse data from various sources, including the sociocultural and ontogenetic domains, namely data extracted from secondary sources on the history of mathematics, mathematical analysis of subconstructs of rational numbers, analysis of textbooks for the middle and high school, as well as textbooks for higher education, research data on students' alternative conceptions, interviews with 3 teacher educators and 4 in-service teachers from middle and high school. Such data allowed us, by means of an active interpretation of the researchers, to list 11 themes from which the rational numbers can be signified and to organise them into an epistemological matrix. Finally, we conduct a theoretical discussion that compares our epistemological matrix with an already quite widespread perspective in mathematics education, which is Kieren's subconstructs.