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?
Answer
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.
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