Not in the sense of geometry where the side of the Moon facing us is EXACTLY 50 percent of the full surface of the Moon. A perfect New Moon only happend when the Moon is EXACTLY between the Sun and the Earth as during a total solar eclipse. The perfect Full Moon only happens when the Moon is exactly opposite the Sun from the Earth, which only happens during a total lunar eclipse. In the later case, the Earth's shadow will occlude the Full Moon's disk; but moments before and moments after the Earth's shadow passes, the Moon would be essentially 50 percent illuminated. I would say that the most Full Moons represent an illumination of better that 49 percent of the Moons full surface, and better that 98 percent of the hemisphere facing the Earth. To the eye, however, anything over 90 percent illumination looks like a Full Moon!