The Sheiris Hapeleitah explains this precise measurement as follows: The Gemora in Bava Basra (73b) states that Mount Tabor was four parasangs (parsa’os) high. A parsah is four mil. A mil consists of two thousand amos. Accordingly, a parsah is eight thousand amos. It emerges that Mount Tabor is thirty-two thousand amos high. Chazal tell us that Mount Sinai was five hunred amos tall, which is precisely one sixty-fourth of Mount Tabor.
The following question may be asked: If the Holy One, Blessed be He did not wish to give the Torah on Mount Tabor, for it was haughty, why did He give the Torah on a mountain at all? The Torah could have been given on a flatland, where there would be no concern for haughtiness whatsoever! It was given on Mount Sinai, a mountain which its height was one sixty-fourth of Mount Tabor to teach us that a Torah scholar should possess this small measure of haughtiness.