Gemara

(Mishnah - R. Yosi ha'Gelili): If Reuven's sheep (a Mevakeres) gave birth to twins, and their heads left the womb at the same time, both are (Kadosh and are) given to Kohanim - "ha'Zecharim la'Shem."

Chachamim say, Iy Efshar Letzamtzem (two things cannot be made exactly equal);

Therefore, he keeps one of them. He gives the other to a Kohen.

(D'Vei R. Yanai): R. Yosi ha'Gelili holds that Efshar Letzamtzem b'Yedei Shamayim, and all the more so b'Yedei Adam.

Question: Chachamim hold that Iy Efshar Letzamtzem b'Yedei Shamayim. What is their opinion about b'Yedei Adam?

18a - Answer (R. Chiya bar Avin - Beraisa - R. Eliezer): If a murdered body was found equidistant from two cities, each of them brings an Eglah;

Chachamim say, they bring one Eglah and stipulate (that it is for the closer city).

This shows that they hold that Iy Efshar Letzamtzem, even b'Yedei Adam.

Bava Metzi'a 52b (Chizkiyah): One may redeem Ma'aser Sheni worth less than a Perutah, and its Chomesh (an extra quarter of the principal), on prior coins (on which Ma'aser was already redeemed), for surely he was not exact.

Erchin 29a (Shmuel): If Hekdesh Shavah Maneh (worth 100 Zuz, which is a large amount) was redeemed onto a Perutah, the Hekdesh becomes Chulin.

This is b'Di'eved when the Mikdash stands, for then there is a loss to Hekdesh;

Nowadays, without a Mikdash (in any case we get rid of the money lest someone transgress Me'ilah) this is l'Chatchilah.

Rishonim

Rambam (Hilchos Ma'aser Sheni 2:2): Ge'onim ruled that nowadays l'Chatchilah one may redeem Shavah Maneh on Shavah Perutah. This should not be more stringent than Hekdesh, all the more so one may do so for Ma'aser. He casts the Perutah to the sea.

Ra'avad: I would be astounded if the Ge'onim said so even nowadays Peros on Peros, except for Ma'aser Sheni of Chutz la'Aretz, which they made like Demai.

Rambam (5:6): If one redeems Ma'aser for more than it is worth, the excess does not get Kedushas Ma'aser.

Kesef Mishneh: The Yerushalmi says so.

Ri Korkus: The Yerushalmi says that if one redeems Hekdesh for more than its value, the excess gets Kedushas Ma'aser, for people are prone to be Makdish more.

Ritva (52b DH Gufa): Chizkiyah holds that one redeems with intent that if later he will redeem more Ma'aser on the excess, it will become Kodesh then, and if not, it is Kodesh now. Rashi says that mid'Oraisa, less than a Perutah cannot be redeemed. This is wrong. If so, Chachamim would not enact that it becomes Chulin! Rather, mid'Oraisa one may redeem it on previous coins, or let it rot. Chizkiyah teaches that Chachamim obligate redeeming it on prior coins.

Question (Tosfos 53a DH Dilma (2)): When one redeems on Perutos, that exact number of Perutos of Ma'aser is redeemed, but no more. Why does the Mishnah (2:8) allow this? Whatever Ma'aser remains above a whole number of Perutos will be eaten without redemption!

Answer #1 (Tosfos): One may redeem onto an Isar and Perutos together. (One can redeem on an Isar any amount between a Perutah and the entire value of the Isar.) There, we do not decree lest he redeem on Perutos alone, for people know that a half-Perutah cannot put Kedushah on a coin.

Answer #2 (Tosfos ha'Rosh DH Chetzi): We said that one cannot calculate the exact value of Ma'aser Sheni, i.e. without exertion, and one would not do so for a whole stack. When one wants to be exact, he can, and this suffices, for the Torah was given to mortals.

Poskim

Shulchan Aruch (YD 331:133): Nowadays, if one wants to redeem Shavah Maneh of Ma'aser on a Perutah, l'Chatchilah, he does so, and casts the coin to the sea. Similarly, if he redeemed Shavah Maneh of Ma'aser on Shavah Perutah of other Peros, it is redeemed, and he burns the other Peros, lest there be a Takalah to others (lest they eat them without Pidyon).

Gra (Shnos Eliyahu, Ma'aser Sheni 2:9, Perush ha'Aruch): Chachamim permit redeeming only three times on Kesef, i.e. Peros on (copper) coins, coins on silver, and silver on coins.

Minchas Shlomo (1:66): Many people designate a silver coin and redeem their Ma'aser on it many times, each time on a Perutah, until the coin is full with Kedushas Ma'aser. Then, they redeem it on a Perutah on another coin, and when the latter coin is full, they redeem it on a Perutah on the first coin or another coin, and do so forever. (Some are stringent not to redeem more than three times on Kesef, due to the Gra's opinion.) Even if the two coins are the same weight and mintage, it works, for nowadays l'Chatchilah one may redeem Ma'aser Shavah Maneh on a Shavah Perutah. The Poskim explain that Ma'aser Sheni is no more stringent than Hekdesh, for which Shavah Maneh can be redeemed on a Shavah Perutah. This is because Ona'ah does not apply to Hekdesh (Bava Metzi'a 57a). However, we can say that this is only when Shavah Maneh is redeemed on a Perutah or Shavah Perutah, for this is like a sale. Perhaps it does not work when Kesef is redeemed, and all the more so if the two coins are the same weight and mintage, we cannot redeem a full Maneh on a Perutah of another Maneh.

Also, perhaps the law that one may redeem Ma'aser Shavah Maneh on a Shavah Perutah depends on the argument of R. Meir and R. Yehudah about whether Ma'aser is Mamon Gavoha (Hash-m's property). Seemingly, we equate Ma'aser to Hekdesh only because we hold that it is Mamon Gavoha, so it is like Hekdesh. According to R. Yehudah, we can say that it is redeemed only on its value. However, perhaps even R. Yehudah agrees, for we this is not afflicting "your brother" or "fellowman." If so, he can agree that regarding Ona'ah it is like Hekdesh. R. Shlomo Sirili'o explains that this is why one may redeem Shevi'is Shavah Maneh on a Shavah Perutah, even though all agree that Shevi'is is commoners' property. (However, this requires investigation why we are lenient to rely on this nowadays more than when the Mikdash stood. The Gemara says that then, it was forbidden to redeem Shevi'is on a small value.)

Question (Minchas Shlomo DH Ach): Why does the Rambam hold that if one redeems Ma'aser for more than its worth, the excess does not get Kedushas Ma'aser? Since Ma'aser is like Hekdesh, there is no Ona'ah. Just like one can redeem a Maneh on a Perutah, one should be able to redeem Ma'aser on more than its value! The Rambam does not distinguish between when Hekdesh or the person was afflicted (underpaid or overcharged). R. Yochanan taught this law in the Yerushalmi. R. Yonah said that this is according to the opinion that Ma'aser is Mamon Hedyot (people's property), but according to the opinion that it is Mamon Gavoha (all the money gets Kedushah). R. Asi said that it is because a person is wont to give too much Hekdesh. The Pnei Moshe and Gra explain that even according to the opinion that it is Mamon Gavoha, regarding Ma'aser Sheni a person does not intend to redeem for more than the value. This connotes that only when one redeems Stam, the excess does not get Kedushah, but if he explicitly intended to redeem for more, everything gets Kedushah. If so, why did the Rambam write Stam that the excess does not get Kedushah, which connotes in every case?

Answer (Minchas Shlomo): It seems that the Rambam holds that since one cannot make Ma'aser through a Neder (vow) or Nedavah (voluntarily), and one who takes too much Ma'aser, his Ma'aser is messed up, therefore also through redemption one cannot be Matpis (imbue with Kedushah) more than the Ma'aser is worth. Even so, the Yerushalmi suggested that if it is Mamon Gavoha, granted, one cannot intentionally redeem for more than the value, but if he erred about the value, the entire amount should be Nitfas. We find regarding separation of Ma'aser that even though it is best to weigh, one may tithe through measuring or counting, and we do not say that he gives too much or too little, and so his Peros or Ma'aser are messed up. This is because even when one weighs, he cannot give the exact amount, and still his Peros and Ma'aser are fine, because the Torah was not given to angels. Therefore, one may tithe even through measure or number. The same applies to Ona'ah. We should say that any amount is Nitfas, since it is the way of business (to err). The Yerushalmi answered that one intends that the excess not be Nitfas. It seems that Ma'aser is unlike Hekdesh, for he knows that he himself will eat the Ma'aser, and any excess Ma'aser does not benefit 'Hekdesh'. Also, not being Matfis the entire amount enables him to redeem Ma'aser worth less than a Perutah on what remains in the coin. He is not concerned for this regarding Hekdesh, for perhaps he will never need to redeem Hekdesh again. Also, we have no source for redeeming less than Shavah Perutah of Hekdesh on coins used to redeem previously.