Ma'aser Sheni, Chapter 4, Mishnah 8. This mishnah deals with the details of calculating the amount of ma'aser sheni that may be redeemed with a given coin.
A change in the coin's value from place to place:
"HaManiach issar v'achal alav chetzyo" - a person designates an issar coin for the redemption of ma'aser sheni. The issar consists of eight perutos, and he ate against half of its value, food worth four perutos.
"V'halach l'makom acher v'harei hu yotzei b'pundyon" - in the new place the coin's value is doubled, since a pundyon is two issarin. It turns out that the original coin is worth two issarin here, and even though he already ate against half of it, the remaining half is now worth a full issar.
"Ochel alav od issar" - therefore he may eat against it an issar's worth, and not merely half an issar's worth, because its value has risen.
And in the opposite case:
"HaManiach pundyon v'achal alav chetzyo" - he set aside a pundyon, which is worth two issarin, and ate against half of it - produce worth one issar.
"V'halach l'makom acher v'harei hu yotzei b'issar" - in the new place the pundyon's value has dropped by half, so that it is worth only an issar.
"Ochel alav od pelag" - he may eat only half an issar's worth. In his original place he still had an issar's worth left, but once he moved to a place where its value is half that amount, he is left with only half an issar's worth to eat against.
When is the coin considered to have been completely redeemed?
The next part of the mishnah deals with someone who holds a coin of ma'aser sheni and eats produce on the strength of that coin. At what point is the coin considered fully redeemed, that it has been entirely used up and no longer carries the sanctity of ma'aser sheni? In other words, how much produce must he eat against the coin until the remainder left in it is so negligible that he may use the coin as ordinary money?
"HaManiach issar shel ma'aser sheni, ochel alav achad asar b'issar v'echad m'meah b'issar" - one who set aside an issar coin of ma'aser sheni eats against it up to one eleventh of an issar, or up to one hundredth of an issar. What are these two measures?
One eleventh: this refers to ma'aser sheni of demai, produce that we do not know for certain was tithed, that was bought from an am ha'aretz, someone who is not careful with the laws of tithes, and out of stringency we separated ma'aser sheni from it again. With ma'aser sheni of this sort, he may leave over up to one eleventh.
One hundredth: with definite ma'aser sheni, produce that is certainly ma'aser sheni, that is not enough; rather, no more than one hundredth may remain.
What does this mean? For example: eleven pomegranates are sold for an issar. Once he has eaten ten pomegranates with the sanctity of ma'aser sheni and under the conditions of ma'aser sheni, that one eleventh of the issar against which he could have eaten one more pomegranate as ma'aser sheni need not be eaten. That amount of one eleventh of the coin which remained unredeemed is null and void, and there is no need to be concerned about it and eat the eleventh pomegranate. The same applies to one hundredth: if one hundred pomegranates can be bought for an issar, he must eat ninety-nine, and that last one, one hundredth, is considered nullified.
The dispute between Beis Shammai and Beis Hillel:
That is the first opinion in the mishnah, and it is disputed:
"Beis Shammai omrim: hakol asarah" - everything is based on a single measure of one tenth, and it is enough that he ate nine parts. Both with demai and with definite ma'aser sheni, in both the measure is one tenth.
"U'Beis Hillel omrim: b'vadai achad asar, u'v'demai asarah" - with definite ma'aser sheni the measure is one eleventh, and with demai it is one tenth.
We will not enter into the details of the calculation, only into the basic distinction between these two: when a person redeems definite ma'aser sheni, he must add a fifth, whereas when redeeming ma'aser sheni of demai he need not add a fifth. And the calculation works out that if one eleventh remains in the coin, even together with the added fifth it does not amount to the value of a perutah, and anything less than a perutah is considered worthless. Therefore, since one eleventh together with the fifth does not reach the value of a perutah, there is no need to be concerned about it. And with demai, since he does not add a fifth, one tenth on its own comes out to less than a perutah, and so it is nullified and there is no need to be concerned about it.
In summary: in this mishnah we learned two matters. The first - the change in the coin's value from place to place: if its value rose from an issar to a pundyon, he eats against the remainder an issar's worth; if its value fell from a pundyon to an issar, he eats against it only half an issar's worth. The second - the measure at which the coin is considered to have been completely redeemed: according to the first opinion, with demai one eleventh and with definite ma'aser sheni one hundredth; according to Beis Shammai, one tenth in both cases; and according to Beis Hillel, with definite ma'aser sheni one eleventh and with demai one tenth - because with definite ma'aser sheni the added fifth enters the calculation and with demai it does not, and in both cases the remainder does not reach the value of a perutah and is therefore nullified.