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What degree of precision is necessary when calculating t'rumos and ma'asros?
The mishnayos deal almost exclusively with collections of discrete objects like loaves of bread and crops, but could that just be for illustrative purposes and not an indication of lesser precision?
Does the same apply (when the Beis Hamikdash is not standing) to tithing money?
Terumah Gedolah should not be measured with precision but should be given באומד by estimation. One should not even use a vessel of known measurement to remove the Terumah Gedolah, unless one doesn't fill the vessel to a known line. (Terumot 1:7, Rambam Terumot 3:4)
Maaserot (Rishon, Sheni, Ani, and Min HaMaaser) should be given with high precision. The Mishna (Terumot 4:6) writes:
המונה משובח והמודד משובח ממנו והשוקל משובח משלשתן.
One who counts is [more] praiseworthy [than one who estimates]; one who measures is more praiseworthy than one who counts; one who weighs is more praiseworthy than all three of them.
The Shulchan Aruch (YD 331:24) takes this as referring to a item which can be evaluated in all three ways. If it is usually only evaluated in one of the ways, then that method is sufficient.
Rambam (Maaserot 1:14) summarizes nicely:
וכל המדקדק בשיעור משובח.
Whoever is exacting in measuring is praiseworthy.
It seems there's something special about exactly 10%. R S Taub, The Laws of Tzedakah and Maaser, p122, says that to fulfil "maaser" you should first isolate 10%. The first source is the third footnote Sefer Ahavat Chesed (by the Chafetz Chaim), sec 2, Ch 19, which refers to a "Sod Gadol"/"Great secret", and he also mentions a few other sources I don't recognise. I think he thinks there's something of Kabbalistic significance.
Another idea: Ethics of the Fathers 1:16 means something like "Rabban Gamliel would say 'Get a Rav and remove yourself from doubt and don't tithe approximately any more'". If it's a series of three pieces of advice then the third one might be extended to apply to money. If it's a suggestion with two pieces of justification, we are assumed to think exactness is a virtue in at least some tithes.
