Rough set theory proposes a formal definition of knowledge and provides a series of tools to deal with knowledge. However, in the algebraic representation of this theory, it is difficult to understand the essence of rough set theory, and efficient algorithm of knowledge reduction has not been found. In this paper, a relationship between knowledge and information is set up, and then based on the relationship an information representation of the concepts and operations about rough set theory is given. Finally, the equivalence properties between information representation and algebraic representation of knowledge reduction are proved. These conclusions are helpful for people to understand the essence of rough set theory and essential to seek new efficient algorithm of knowledge reduction.