Transpose analysis on numbers with infinite decimal expansion

This research, product of our process as students of Pedagogy in Mathematics, aims to analyze how the concept of numbers with infinite decimal development is treated, specifically those with periodic or semi-periodic decimal expansion, or commonly called periodic or semi-periodic decimal numbers in Chilean school literature. From Yves Chevallard's Anthropological Theory of Didactics, we will see if the mathematical significance of the concept is respected and we will design a more complete teaching proposal for these numbers.