Decimal fractions are the practical system of notations representing real numbers. The set of decimal fractions with the definition of comparison of decimal fractions and the identification of their double representations is essentially the field of real numbers. Therefore, we have to clarify the concept of decimal fractions. However, there are problematics that the aquisition of the concept of decimal fractions is not easy. In this paper, we attempt to eradicate the problematics relevant to the acquisition of decimal fractions discussed above and find the desirable direction of instruction of meaning for mathematical symbols: The case of decimal fractions. In J. Hiebert & decimal fractions. First of all, we clarify the essence of them - ratio, operator and linearity. And we compare and analyse the theories about decimal fractions of Resnick, Drexel, Brousseau and Hiebert and the contents of texts about decimal fractions in Korea. Finally, we suggest the efficient instruction methods which are faithful to the essence of decimal fractions and choose some methods among them to plan the classroom instruction and implement the methods in the classroom.