Okay, so I know this is probably going to sound like a pointless question, since it's just about numbers of people in Numbers, and population censuses are usually rounded off anyway, but why do the rules change thoughout the taking of the census?
What I mean is, when Moses talleys up all the men over age 20 of the twelve tribes, excluding the Levites, in Numbers 1, he specifies population counts to the nearest 50's, like in the grand total being 603,550.† And then when he talleys up all the men over the age of 1 month of the Levites, the count of the families of Gershon (7,500), Kohath (8,600), and Merari (6,200), he specifies to the nearest hundred, which could also be argued was rounded to the nearest 50.†The problem I don't understand is that when Moses talleys up the three families of the Levites together, he only specifies to the nearest thousand (22,000), when actually the number should be 22,300.† Now this is a census, so of course, censuses aren't always 100% accurate, so that extra three hundred could have just been dropped off, and that would be okay.† But then when the Levites are dedicated instead of the firstborns, Moses decides to specify to the nearest 1 person, being as specific as 22,273. And the Lord speaks to Moses and says that because there are 273 more firstborns than the Levites, then extra redemption has to be made for the extra 273 firstborns.† But considering that the Levites should have been added up to 22,300 instead of a less specific 22,000, in all actuality there weren't 273 more firstborns than there were Levites, but rather there were 27 more Levites than firstborns.† So the extra redemption thing kind of makes no sense.
Now I know that nitpicking about the census really shouldn't be all that important when you think about the overall picture that the message is trying to convey in that specific passage, but it just seems like whenever I don't pay attention or understand why the rules change or why there are exceptions for certain things, then I miss some huge, important detail, which is necessary for understanding the overall message.
The first census took place at the base of Mount Sinai, just after the Law was given and the tabernacle was erected and before they began their journey to Canaan. The rules for the census were: "every male individually, from twenty years old and above, all who were able to go to war" (Numbers 1:20), so in other words, this was a count of the potential size of Israel's army. The Levites weren't included because they would not be going into the battles.
The census of the Levites also took place at Mount Sinai, but it was a bit later -- after Nadab and Abihu had died (Numbers 3:4). God told Moses, "Now behold, I Myself have taken the Levites from among the children of Israel instead of every firstborn who opens the womb among the children of Israel. Therefore the Levites shall be Mine, because all the firstborn are Mine. On the day that I struck all the firstborn in the land of Egypt, I sanctified to Myself all the firstborn in Israel, both man and beast. They shall be Mine: I am the LORD" (Numbers 3:12-13). For this census all males 1 month old and older were counted. The total is stated as being 22,000 which doesn't match the sum of the parts. One of the better possible explanations was written by Adam Clarke:
"This total does not agree with the particulars; for the Gershonites were 7,500, the Kohathites 8,600, the Merarites 6,200, total 22,300. Several methods of solving this difficulty have been proposed by learned men; Dr. Kennicott's is the most simple. Formerly the numbers in the Hebrew Bible were expressed by letters, and not by words at full length; and if two nearly similar letters were mistaken for each other, many errors in the numbers must be the consequence. Now it is probable that an error has crept into the number of the Gershonites, Nu 3:22, where, instead of 7,500, we should read 7,200, as ך caph, 500, might have been easily mistaken for ד resh, 200, especially if the down stroke of the caph had been a little shorter than ordinary, which is often the case in MSS. The extra 300 being taken off, the total is just 22,000, as mentioned in the 39th verse" [Adam Clarke Commentary].
Two other possibilities is that the final number was rounded (not likely), or that 300 of the total were firstborns who already belonged to God and shouldn't be counted as a part of the substitutes for the firstborns (if that was true, 300 seems to be too low of a number for firstborns among 22,000 men).
A count of the firstborns males in the rest of Israel, one month and older came to 22,273. Since the difference is stated to be 273 (Numbers 3:46), this is further evidence that one of the division counts earlier was off by 300 due to a copyist error.
Why hasn't the apparent error been fixed? Simple, the people who examine manuscripts want to have accurate copies. They won't make changes, even to fix what appears to be a simple mistake without rock solid evidence. So probably until someone finds a really old copy of the Hebrew with the numbers being different, the scholars will wait rather than accidentally inserting another error in trying to fix an what they are fairly certain was an earlier error.