Based on the words zeh Keli v’anveihu the Talmudic Sages deduced that one should strive to perform mitzvahs in an aesthetically pleasing manner. This applies to various mitzvahs, including the tallit you wear. Not only should the tallit be attractive, but the tzitzits, too – which of course are the essence of the mitzvah – should look nice.
Keeping your tzitzits clean and fully intact is not always easy (and is never easy if you have small children who wear tzitzits). To keep your tzitzits clean, check often to make sure they don’t drag on the ground when you sit, stand or walk.
Tzitzits sometimes fray when they are brand new if you cut them after tying to even out the lengths. (Be sure you do not cut them to a length of less than 12 thumb-widths, from the first knot near the corner to the tips of the tzitzits.) To prevent further fraying, you can try any of three tips (no pun intended):
- Dip the ends in nail polish.
- Dip the ends in wax. You can even use the wax drippings from Havdalah. There is a Talmudic precept of taking an object used to perform a mitzvah and using it to perform another mitzvah. (Spiritual recycling/reuse.)
- Tie a small knot at the end of each string (see Shulchan Aruch O.C. 11, 4).
Some tzitzits strings (including the hand-spun tzitzits I sell) are made with reinforced ends to prevent fraying.