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Tithing is an Old Testament practice, mandated in the Law given through Moses, and is not binding on believers today. Having said that, tithing is not a bad bench-mark to use when considering how much to give. Note that the tithe today would include any and all charitable donations not just those given to a church.
You must realize, however, that there is no mention of tithing being binding on believers in the New Testament. However the Bible does talk about tithing in the Old Testament which was a law binding on God's people while the law was in effect, that is, until the crucifixion and resurrection of the Lord.
Here's a passage in the Old Testament, Leviticus 27:32 which defines the "tithe" "And concerning the tithe of the herd, or of the flock, even of whatsoever passeth under the rod, the tenth shall be holy unto the LORD." The word "tithe" in the Hebrew of the Old Testament and the Greek of the New Testament literally means "a tenth" which is 10%.
The "tithe" under the law of Moses is no longer in force for New Testament believers. Our offerings are the equivalent of "freewill offerings" under the law - these were voluntary and involved no set amount. In Christ, nobody has the right to tell us how much to give or to whom it should be given. In Christ, we acknowledge that all that we have belongs to God including ourselves, not just 10%.