Normalizing a quaternion
Solution 1:
Yes, by its length or norm as it's also called.
You get:
$$U_q=\frac{w}{d} + \mathbf i \cdot \frac{x}{d} + \mathbf j \cdot \frac{y}{d} + \mathbf k \cdot \frac{z}{d}$$
where $d = ||q|| = \sqrt {w^2 + x^2 + y^2 + z^2} $ is the norm.