Light from a point source strikes a small area oriented...

The illuminance $E$ on a small area is given by $E = \dfrac{I}{r^2} \cos \theta$, where $\theta$ is the angle between the normal to the area and the direction of the incident light.

Initially, the area is perpendicular to the incident light, which means the normal to the area is parallel to the incident light. Thus, \theta = 0^{}^{{}^{\circ}}.

When the area is rotated about the incident light, the axis of rotation is the incident light ray itself. Rotating a perpendicular surface around its own normal does not change its orientation relative to the incident light.

Therefore, the angle $\theta$ remains 0^{}^{{}^{\circ}} and the illuminance remains unchanged.

Since there is no change in illuminance, the fraction by which the illuminance changes is $0$.