Round and Square Numbers In the Bible

My weekly halachah column for parashas Bemidbar:

In the censuses of parashas Bemidbar and parashas Pinchas, the population totals for almost all the tribes are multiples of one hundred, except for those of the tribe of Gad in the former census and the tribe of Reuvein in the latter. Several commentators assume that these figures are not exact, and that the Torah is rounding (Meshech Chochmah 3:16, Tosefes Brachah to Bemidbar). The earliest known proponent of this view, R. Yeshayah of Trani (cited in Penei David), provides two other Biblical examples of rounding: the Torah (Devarim 25:3) prescribes the punishment of a sinner to be forty stripes, but the Oral Tradition explains that only thirty-nine are actually administered, and the Torah (Vayikra 23:16) commands us to count fifty days between Pesach and Shavuos, but of course, we only count forty-nine.

The Rosh (at the end of Pesachim) asserts one other example of this latter sort of rounding, where a number one less than a multiple of ten is rounded up by one to the multiple of ten: the Torah (Bereishis 46:27) relates that “all the souls of the house of Jacob, which came into Egypt, were threescore and ten” (but only sixty-nine are enumerated). This claim that the discrepancy can be understood as the product of rounding is problematic, however, as the same discrepancy is manifest with regard to the subtotal of thirty-three that the Torah gives for the descendants of Leah, while only thirty-two are enumerated. Here the idea of rounding is inapplicable, and we must seemingly resort to one of the other suggestions offered by the Talmud and the various commentators: the totals include Yocheved, who was born just they entered Egypt (but not earlier, and so is not mentioned in the earlier enumeration – Bava Basre 123a-b), or Yaakov himself (Ibn Ezra, as well as many of the Tosafists), or even Hashem Himself (Da’as Zekeinim Mi’Ba’alei Ha’Tosafos).

In a classic example of the aharonim being “frummer” than the rishonim, despite the fact that the one rishon known to have discussed the point, Rav Yeshayah di Trani the Elder (the Rid), takes for granted that the Biblical figures are rounded, Rav Ya’akov Yisrael Kanievsky (the Steipler) is reported by R. Ozer Alpert to have rejected this notion out of hand:

Rabbi Chaim Kanievsky relates that he initially assumed that the census numbers were rounded, but when he mentioned this to his father, the Steipler responded that a number written in the Torah must be exact, and God must have had a reason why He miraculously caused each tribe to have such even numbers of people.

My weekly lectures for Bemidbar on this topic, along with their handouts, are available at the Internet Archive.