Gemara

(Beraisa): One may buy Asiris ha'Eifah (the volume of 43.2 eggs of fine flour, for a Korban Minchah) for a Perutah.

(Rava): The Tana learns from a poor Yoledes. She brings a bird (which costs 24 Perutos) for 1/32nd of the (price of the) Korban it replaces (a lamb). Likewise, Asiris ha'Eifah of Dalei Dalos is 1/32nd of the (cheapest) price of Korban Oni.

Letter of the law, Asiris ha'Eifah may be bought for three quarters of a Perutah. However, it is improper to pay less than a Perutah for a Korban.

Menachos 59b (R. Yitzchak bar Yosef): If a k'Zayis of Levonah was put on a Minchah, it is Pasul.

(R. Yochanan): "V'Lo Yiten connotes a proper Shi'ur.

Bava Metzi'a 31b - Question: Perhaps "Nason Titen" is only if you can give a big gift. What is the source that it applies even to a small gift?

Answer: "Nason Titen" teaches any case.

Gitin 12a (Rav): If one makes Hekdesh his slave's hands, the slave borrows money for food, and pays up the debt through his earnings.

12b - Question: How can he pay his debt through his earnings? Every bit of money he earns becomes Hekdesh immediately!

Answer: He pays from his earnings bit by bit, before his earnings accumulate to a Perutah.

Bava Basra 9a (Beraisa): If one begs from door to door, we do not give to him from the Kupah.

A poor person begging from door to door came to Rav Papa. He did not give to him.

Rav Sama brei d'Rav Yeiva: If you do not give to him, no one will, and he will die!

Question: The Beraisa says that we do not give to him!

Answer: We do not give to him a large amount, but we give a small amount.

Pesachim 32b (Beraisa): If a Zar ate a k'Zayis of Terumah (b'Shogeg), he pays Keren v'Chomesh;

Aba Sha'ul says, he pays only if he ate the value of a Perutah.

The first Tana learns from "v'Ish Ki Yochal Kodesh bi'Shgagah." The Shi'ur of 'Achilah' (eating) is a k'Zayis. Aba Sha'ul's learns from "v'Nosan (la'Kohen Es ha'Kodesh)." The Shi'ur of 'Nesinah' (giving) is a Perutah.

Chulin 137b (Mishnah): One who shears his sheep must give to the Kohen five Sela'im of Yehudah (this is ten of Galil).

Question: Rav and Shmuel taught that one must give one part in 60 of Gez (shearings), Terumah, and Pe'ah. (Rav obligates giving from a Maneh and a half, but a 60th part is less than a Sela!)

Answer (Rav and Shmuel): The Mishnah teaches that if a Yisrael has much shearings and wants to give them to more than one Kohen, he must give to each Kohen five Sela'im.

138a (Mishnah): The shearings must weigh five Sela'im, in order that the Kohen can make a small garment.

(R. Yehoshua ben Levi): We learn from "La'amod Leshares" - it must be fitting to make a garment that a Kohen serves in, the Avnet (belt).

Kesuvos 67b (Beraisa): We give to an Oni "what is lacking to him", even a horse to ride on and a slave to run in front of him.

Rishonim

Rashi (Gitin 12b DH b'Fachos): The slave pays from his earnings before they accumulate to a Perutah. Hekdesh does not take effect on less than a Shavah Perutah.

Tosfos (12b DH Pachos): A Mishnah teaches that a Perutah is the Shi'ur for five things. According to Rashi, it is the Shi'ur also for Hekdesh to take effect! The Ri says that (Hekdesh can take effect on less than a Shavah Perutah;) here, the owner intended that it take effect only on a Perutah (to enable the slave to borrow and pay).

Torah Lishmah (241): If one was Makdish his slave's hands, the slave borrows, and pays the debt through his earnings. We asked that whatever he earns becomes Hekdesh immediately, and answered that he pays bit by bit, before his earnings accumulate to a Perutah. Rashi holds that Hekdesh does not take effect on less than a Shavah Perutah. If so, one who vowed cannot exempt himself with less than a Perutah. Even according to Tosfos, who holds that Hekdesh can take effect on less than a Shavah Perutah, one who vows does not intend for less than a Shavah Perutah. Likewise, one who pledged oil did not intend for less than a Shavah Perutah. Hekdesh takes effect on less than a Perutah only if one explicitly did so.

Note: Perhaps Stam, Hekdesh takes effect on less than a Perutah. A master intends that it will not, to enable his slave to borrow and pay! Since we permit Stam, even when the master is ignorant and does not know the law, we cannot say that it is due to special intent.

Tosfos (Pesachim 32b DH v'Ein): Aba Sha'ul holds that 'Nesinah' is at least a Perutah. Chachamim disagree only because it says 'Achilah'. We hold that one piece of wheat exempts the entire stack (for Terumah), even though it says 'Nesinah'! We acquire with a Kli even though it is worth less than a Perutah, even though it says "he gave to his fellowman." A Get on Isurei Hana'ah is Kosher, even though it says "v'Nasan b'Yadah." We can answer that Nesinah of payment must be a Perutah, like returning theft, which must be at least a Perutah. Other places (that are not payment), even though it says Nesinah, do not require a Perutah. In Kerisus (6b), regarding putting Shemen ha'Mishchah on a Zar, R. Yehudah learns from Terumah to require a k'Zayis. He should be stringent to say that it is any amount, like we find regarding Zerikah, and putting blood and oil on the thumbs and toes of a Metzora, which is like anointing. This is not difficult for the opinion that argues with R. Yehudah and obligates for any amount.

Maharsha (Chidushei Agados Bava Metzi'a 31b DH Nason): 'Nesinah' connotes an important amount. In Chulin, we learn from "Titen" that there is a Shi'ur how much to give.

Sedei Chemdah (Ma'areches Nun Klal 21): In Chulin is different, for after "Titen" it says "to stand to serve." We would not expound from Titen alone, like Tosfos says. Melei ha'Ro'im (Bava Metzi'a 31b) explains that "Asher Yechsar Lo" teaches whatever he needs, i.e. even a horse to ride or a slave to run in front of him. Therefore, we already know about a big gift, so we expound to teach about a small gift. Bris Yakov says that without a Drashah, we would have learned Tzedakah from all Matanos Aniyim written in the Torah, which is 'until satiation.' Indeed, one who has much must give to satiation. The Torah teaches that even one who lacks this must give even a small gift. Alternatively, the Torah said "do not begrudge" when you give Tzedakah, and promises a Berachah for giving. Presumably these apply only to a large gift.

Poskim

Shulchan Aruch (YD 249:10): It is good to give a Perutah to Tzedakah before each Tefilah, for it says "b'Tzedek Echzeh Fanecha."

Yad Eliyahu (Pesakim 44): One who gives food to an Oni must give a k'Zayis or a Shavah Perutah. What was the Hava Amina in Bava Metzi'a that one must give a large gift? Nesinah always connotes a k'Zayis or Perutah! Also, what was the Hava Amina that if he cannot give a large gift, he is totally exempt?! Also, the Shulchan Aruch brings the Rambam, who say that one is Yotzei with k'Grogeres (the volume of a fig). It seems that usually this is less than a Shavah Perutah, like it says in Kidushin (if one was Mekadesh with dates, sometimes they join to be a Shavah Perutah.) Even though the Torah did not require a big gift, what is the source for less than a Shavah Perutah? In Bava Basra, we say that we do not give to an Oni (who begs from door to door) a large amount, but we give a small amount. The Beis Yosef brings that Rashi and the Tur argue about whether this addresses the Gabai of Tzedakah or individuals. The Mitzvah is on the generation to feed Oniyim begging from door to door. It is not enough of a Mitzvah to exempt one who gives to him from other Mitzvos at the time. If one does not give to him, others will! However, if one is not engaged in a Mitzvah, he has an Aseh to give to him even less than a Perutah.

Torah Lishmah (ibid.): There is another reason why he cannot exempt himself with less than a Shavah Perutah. If one stole less than a Shavah Perutah. even though he transgressed due to a half-Shi'ur, he need not return it. Likewise, there is no Mitzvah to return an Aveidah worth less than a Shavah Perutah. It is not considered money. How can one fulfill the Mitzvah of his vow with it? In Pesachim, Aba Sha'ul holds that 'Nesinah' is at least a Perutah. Chachamim disagree only because it says Achilah. Tosfos asked that we hold that one piece of wheat exempts the entire stack (for Terumah), and we acquire with a Kli even though it is worth less than a Perutah, even though it says "he gave to his fellowman." A Get on Isurei Hana'ah is Kosher, even though it says "v'Nasan b'Yadah." He answered that Nesinah of payment must be a Perutah, like returning theft.

Mishneh Halachos (13:207): Even if one who gives less than a Shavah Perutah did not fulfill the Mitzvah of Tzedakah, he did not transgress the Lav "Lo Sikpotz Es Yadecha", for he stretched his hand to give! R. Yonah concluded 'one should give to the Oni in private, for "Matan b'Seser Yichpeh Af." One fulfills this through giving to a Tzedakah box. Only one who gives to an Oni is not Yotzei with less than a Shavah Perutah, but one who give to a Tzedakah box is Yotzei, for there is no law of 'Nesinah.' (Half-Perutaos of) Me'ilah join even over years, even though Yom Kipur was in between (Kerisus 18b).

Mishneh Halachos: Acharonim argue about whether less than a Shavah Perutah is considered money. Even according to the opinion that it is not money and a person pardons it, this is only regarding Chulin. There is no one to pardon Tzedakah or Hekdesh, so even less than a Shavah Perutah is money, and it joins.