Abstract: Numerical representation is the basis of mathematical abilities. A hot topic about numerical representation is whether there are two distinct numerical representation systems: the small precise number system and the large approximate number system. The article reviewed researches on numerical representations in different fields, and summarized evidences supporting the dissociation between the two systems. Numerical representation within the range of 1~3 had a set-size signature was proposed to base on attention to objects themselves per se. Therefore it was sensitive to perceptive properties of objects, and was precise representations about numerosities. While numerical representation for numbers above 4 had a Weber ratio signature. It was suggested to base on analog magnitudes, and was approximate representations of numerosities. However, evidences from the brain imaging field had not gained agreement on this issue. At last, the article brought forth the potential questions about the two basic numerical representation hypothesis

Key words: numerosity, precise representation, subitizing, approximate representation, spatial attention