Yes, here is an example for that in 2 dimensional space:
Let vector A be a vector with its initial point at the origin and terminal point at (4,0), such that A = (4,0). Then we have z = (4^2 + 0^2)^(1/2) = (4^2)^(1/2) = 4^1 = 4 and with that u = (4/4, 0/4) = (1, 0). The normalized vector of A does not contain a fraction.
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