Why is the weight of an object on the moon $\dfrac{1}{6}$th its weight on the earth?

The moon's gravitation force is determined by the mass and the size of the moon.

The mass of moon is $\dfrac{1}{100}$ times and its radius $\dfrac{1}{4}$ times that of earth. As a result, the gravitational attraction on the moon is about one sixth when compared to earth. Hence, the weight of an object on the moon is $\dfrac{1}{6}$th its weight on the earth.