Actually, it's weird that all three browsers I tried can display that symbol just fine; that character isn't traditionally present in Mac fonts, whereas a lot of Windows fonts have it. I assume it is because that is a Unicode 1/2 character, so OSX knows how to display it (just as, with proper coding, you can put Japanese right into the middle of any document in OSX, or display Japanese characters inline in a web page in any browser that is Unicode aware). Could also just be that OSX's handling of mapping characters not present in the current font into one that does have it has gotten better.
MS Word, in any case, is NOT very good about handling mixed/non-English character sets or nonstandard characters, and can't deal with Unicode properly, so it doesn't surprise me in the least that it doesn't work properly. The solution is, as telecomm said, to use Equation editor, though if you can find a font that specifically includes the 1/2 glyph, you can type that particular character in that specific font, and it should work.