Rational dimension refers to the dimension of a vector space over the field of rational numbers. It is the minimum number of linearly independent vectors needed to span the entire vector space. The rational dimension can differ from the ordinary dimension of a vector space if the vectors are over a field other than the rational numbers.

The Fourth dimension in Space is a real distance dimension r, completing the three vector displacement dimensions. Space is a quaternion with one real dimension and three vector dimensions, s= r + Ix + Jy + Kz, where I,J and K denote the vector dimensions. The real dimension r is related to time by r=ct where c is the speed of light.

Einstein and Minkowski proposed in Relativity Theory a defective four dimension Space, where the fourth dimension is a vector Ict . This Space is essentially a two dimensional Space and does not exhibit the non-commuttive features of the quaternion Space.

Three - one for each dimension of space. Or four, if you need a time component as well.

The fourth dimension is not "time'. The fourth dimension is a real space dimension r=ct, where c is the speed of light and the fourth dimension r is the product of 'c' and time which gives a real number distance. The other three dimensions are vector dimensions V= Ix + Jx + Ky. The vectors I, J and K are unit vectors with the vector property I2=J2=K2=IJK= - 1.

So, all the dimensions are units of space!

A zero vector is a vector whose value in every dimension is zero.