A system of unit is said to be coherent when all units are either fundamental unit or derived units with numerical value equal to one.
Ex: 1 N = 1 kg m/s2
A system of unit is said to be rational if it can be used to measure the very small quantity and very large quantity.
A system of unit is said to be metric when all units are fundamental units i.e length , mass and time.
SI unit of system follows all above mentioned condition so we can say that SI unit is coherent, rational and metric system of unit.