Q. I’m confused about this issue of whether to add a space after the abbreviation “w/” (with). A previous answer said that there should be a space because the abbreviation stands for a full word, which would have a space after it if written out. But CMOS 6.116 shows no spaces around a slash that stands for “per” or that is used in an abbreviation like “c/o” (in care of) or “n/a” (not applicable). So why is “w/” treated differently?
A. In an expression like “km/s” (kilometers per second) or “$450/week” (450 dollars per week), the slash is a stand-alone abbreviation for “per.” If you were to add a space in either of those expressions, you’d need two of them (one before and one after the slash). In an expression like “c/o” or “n/a,” the slash is a kind of shorthand that tells readers to interpret the letters as abbreviations; it belongs equally to both letters.
The abbreviation “w/” is very much like “c/o” and “n/a” but with only one rather than two abbreviated letters. (Each of those could be written instead with periods, but the slash nonetheless became the convention.) But whereas c pairs with o and n with a, that w is, as our original answer suggested, a single entity that doesn’t normally pair with anything, so it’s usually separated from what comes next by a space.
That’s the editorial logic anyway. The abbreviation “w/” is casual. Any rule regarding its use should be taken w/ a grain of NaCl (and with the understanding that no rule is w/out exceptions).