Using the Prime Symbol
The prime is a short stroke that slants to the right, placed after a number or a letter. In measurement it stands for feet and, as a double prime, inches: someone who is 5′11″ is five feet eleven inches. In angles and coordinates the same pair means minutes and seconds of arc, so 40°26′46″N is a latitude read as forty degrees, twenty-six minutes, forty-six seconds north. In mathematics f′(x) is the first derivative, f″(x) the second, and a primed variable x′ is simply "x prime", a related quantity. Chemists and musicians use primes too, for numbered atoms in a molecule (the 3′ end of DNA) and for octaves in Helmholtz pitch notation (c′ is middle C).
Prime, apostrophe, quote
Keyboards have no prime key, so people type an apostrophe for feet and a straight double quote for inches, and in casual chat that is fine. The trouble starts when software "smartens" the marks: the apostrophe turns into ’, which curls like a closing quote, and the double quote becomes ”, so a height reads as 5’11” with two mismatched hooks. A true prime is straight and slanted, never curled, and it is the same width as a digit's stroke. In anything typeset — a résumé, a listing, an engineering drawing — use the real character or turn off smart quotes before typing the substitute.
Spacing and position
Attach the prime directly to the number with no space: 6′2″, not 6 ′ 2 ″. When feet and inches appear together there is no space between them either. Coordinates run degrees, minutes, seconds with no spaces and the hemisphere letter last, and the degree symbol page covers the first part of that trio. In LaTeX the apostrophe key inside math mode produces a correct prime automatically, so f' is all you need.
Typing it
Windows has no Alt code for the prime; in Word type 2032 and press Alt + X, or use the Win + . emoji panel. Mac users open the Character Viewer and search "prime". Phones have no key, and the smart-quote substitute is usually what people see, so a text replacement that turns ft and in into ′ and ″ is worth setting up if you type measurements often. The character belongs to the General Punctuation block and renders in every mainstream font, though in a monospaced or pixel font it can be hard to tell from an apostrophe.
Transliteration
Scholars transliterating Russian and other Cyrillic languages use a prime-like mark for the soft sign ь, as in Gogol′ or oblast′. Unicode gives that job to the modifier letter prime ʹ, a separate character that behaves as a letter for sorting and searching, which is why library catalogues insist on it rather than the punctuation prime.
In profiles
Height in feet and inches is one of the most typed measurements on dating apps and sports bios, and a correct 6′1″ instead of 6'1" is a small mark of polish. The prime also fits the tidy look of the numero sign and per mille symbol in a "spec sheet" style bio, and sports accounts use it for match minutes, as in "goal 90′+3".