I actually saw a dvar torah this week that claimed that the tribe of Gad showed that the others were actually exact by a miracle in Mail Jewish (quoted below). See the quote from Rav Chaim Kanievsky below based on what his father the Steipler Rav told him.
Another explanation is that the counts were actually rounded to the nearest fifty or rounded up to the nearest fifty. In that case, the tribe of Gad is not different from the others in the rounding method. It is just that the rounding caused them to end in 50 rather than (1)00. Alternatively, since 50 is the precise middle, it was left as is because of uncertainty which way to round.
Aish.com has this explanation
The Shaarei Aharon quotes the Imrei Noam, who maintains that the Torah
isn't particular about small numbers, and suggests that the census for
each tribe was rounded to the nearest 100. Since the tribe of Gad had
precisely 50 extra people, their count couldn't be rounded either way.
As proof that the Torah rounds numbers, the Imrei Noam cites the
commandment to count 50 days of the Omer even though we count only 49,
and the verse ordering 40 lashes to be given to certain transgressors
even though we give only 39. This is also the position of the Meshech
However, 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.
Mail Jewish also brings up the question and suggests an answer.
From: Sanford Lefkowitz
Date: Sun, May 18,2014 at 12:01 AM
Subject: Census counts
In Parshas Bamidbar, we see the first listing of census numbers by
tribe. One rather anomalous feature of the counts is that 11 of the
12 counts are multiples of 100 and one is a multiple only of 10. One
question this raises is "Are these exact numbers or round numbers?".
If they are round numbers the rounding rule must be 'round to the
nearest 10'. The probability that 11 out of 12 numbers, when rounded
to the nearest 10, would also round to a multiple of 100 is on the
order of one in 10 billion. The same anomaly, 11 out of 12 numbers
being a multiple of 100, also occurs the second time the census counts
are given in Parshas Pinchas. The probability that we would have two
independent counts, rounded to the nearest 10, both producing results
where 11 out of 12 counts round to a multiple of 100 if on the order
of 10-20. This suggests there is something unusual going on here.
Shortly after the Bamidbar tribal count, we are given the count of the
Levi'im, 22,000. That certainly looks like a round number. But
shortly after that, we are given the count of the first born, 22,273
and told that each first born has to be redeemed by a Levi. The Torah
then explicitly asks the question of what happens with the 273
remaining first born. Since 22,273 is clearly not a round number and
the Torah explicitly mentions the number 273, it must be that 22,000
is an exact number. Given the unlikelihood of most of the tribal
census counts being a multiple of 100 and the apparent fact that the
Levi'im count is an exact number, it seems likely that all the tribal
counts are exact numbers.
Why are 11 out of 12 tribal counts multiple of 100 each of the times
the count is given? Here is a speculation. Perhaps the Torah is
trying to call our attention to the anomaly. If all the counts had
been a multiple of 100, that would have been even more unlikely than
11 out of 12 counts being a multiple of
100. But if that had been the case, we might have just assumed they were all being rounded to the nearest 100 and not considered it very
interesting. If the counts had been numbers like 21,906, we might just
say, "OK, that's what the number turned out to be. No big deal". But
by having exactly 11 out of 12 counts be multiples of 100 on two
occasions, the Torah is telling us to take notice. The only way such
an unlikely event could occur is if Hashem is in control. He is
taking care of everything, even down to the population counts.
However, I did find a different explanation at Rounding of Numbers in the Censes of Bnei Yisrael by Rabbi Elchanan Samet which discusses the subject at length and attempts to account for the other countings as well
D. ROUNDING TO HUNDREDS OR TO TENS - ARTICLE BY A. MERZBACH
Thus far our assumption has been that in recording the censes, the
Torah rounds figures to hundreds, as it would seem from the great
majority of those that appear in chapters 1-4. But in section B.
above, we note that there are a few figures in these chapters (and
another one in parashat Pinchas) that end in tens, and not in
hundreds. They are:
a. The tribe of Gad in our parasha 45,650 (1:25)
b. The tribe of Reuven in par. Pinchas 43,730 (26:7)
c. The family of Kehat aged 30-50 2,750 (4:36)
d. The family of Gershon aged 30-50 2,630 (4:40)
What is the reason for these exceptions to the system of rounding to
Prof. Ely Merzbach, of the department of mathematics at Bar-Ilan
University, addresses this question in his article, "The Censes of
Bnei Yisrael in the Desert" (published inthe "Higgayon" - Studies in
Rabbinical Thought, vol. 5, 5761). Here are some excerpts:
"It is always possible to attribute this phenomenon (of exactly
rounded numbers) to a miracle, or coincidence, without any explanation
(as some commentators have attempted to do). But explanations of this
sort are rejected by the major commentators with the simple claim that
a miracle must have some significance, or some benefit.
It seems to me that it is possible… [to explain the phenomenon] based
on the following principles, which refer to fairly large numbers (and
certainly to numbers greater than 5,000).
When the figure obtained is in whole tens (without units), the Torah records it as is, without rounding it.
When the figure obtained is not in whole tens, then the Torah rounds it to the nearest hundred.
The logic behind this system is simple: if a number ending in units
already requires rounding, it is rounded to hundreds (with some small
margin of inaccuracy). But if the figure ends in tens, it is left as
If we examine the data in the Torah, this becomes completely clear. In
each of the two censes of Bnei Yisrael in the desert, 11 out of 12
figures are multiples of hundreds, while one (the tribe of Gad in the
first census, and Reuven in the second one) is a multiple of tens. The
probability of any number ending in zero but not being a multiple of
100 is 9/100. Therefore if any 12 numbers are chosen, we can expect
the incidence of appearance of numbers with this characteristic to be
12 x 9/100 = 1.08. In other words: on average, out of 12 numbers, one
will be a multiple of tens (and not a multiple of hundreds).
Moreover ... the greatest probability exists, once again, when there
is exactly one number of this sort out of 12 numbers… Concerning the
censes of the Levite families we could obtain similar results, but
when the number of data is small (there are only three families), no
statistical test may be applied."
E. ALTERNATIVE EXPLANATION FOR NUMBERS ENDING IN TENS IN CHAPTERS 1-4
Merzbach's two rules for rounding figures explain all four exceptional
figures listed at the beginning of section D. above, and even match
the statistical probability of the phenomenon of the two numbers - the
tribe of Gad and the tribe of Reuven - in the two censes held in the
desert. But the "simple logic" that he employs is actually not so
simple. He writes, "If a number ending in units already requires
rounding, it is rounded to hundreds. But if the figure ends in tens,
it is left as is." We may ask: if a number ending in tens is
considered a round number, then why are numbers ending in units not
rounded to the nearest ten, thereby diminishing the maximal inaccuracy
from 49 to 4? The proposition that "If a number… already requires
rounding, it is rounded to hundreds" is not a mathematical one; it is
a matter of personal taste.
Setting aside for a moment the exception of the tribe of Reuven in
parashat Pinchas, focusing instead only on the numbers in chapters
1-4, we may solve the difficulty of the three exceptional figures
without reliance on Merzbach's two rules.
Now we must deal with the number of the tribe of Gad: 45,650. Why is
this number not rounded to the nearest hundred? Perhaps because it
ends precisely with 50, and therefore cannot be rounded either upwards
But we may suggest a slightly different idea: since the exact number 50 cannot be
rounded, it may itself be considered a rounded number, in
a sense, even within a system of rounding to hundreds. Therefore it is
possible that where the real number is close to fifty, the number is
rounded to 50 rather than to 100 (thereby diminishing the inaccuracy
that would result from rounding to 100).