First, I wage a perpetual battle against cramming the textual units typographically up against the figures. There should always be space between the figure and the unit. This is not an SI standard, but it is a U.S. NIST standard. At least this example properly omits the period after the unit abbreviation. The standard abbreviation for feet is ft and not ft. as it is sometimes rendered informally. But I still often lose the battle when the dimensioned quantity is adjectival; e.g., "There was a 5ft gap in the bridge deck."
1) When using prime notation on imperial units of length, the single prime always - without exception - applies to the number of feet;
Correct. One may write 6 ft 2 in most properly. When using the textual abbreviation for feet, it's most proper to use the textual abbreviation also for inches. When using primes notation, the only textual abbreviation that should properly appear is for the canonical base unit.
2) You've split the notation for the 2 and the ⅛, whereas in the concept you're trying to express, they both apply to the same unit (here, inches: two and one-eighth inches).
Indeed, that's just the height of absurdity. Two different symbols trying to represent the same units in the same expression isn't the least corrected by the feeble, "That's just the way I've always done it." It's just wrong, fully and completely.
We American engineers still occasionally have to work in English units for legacy designs, and because our common parts are very often still provided in round units by English reckoning. Some electronic pin spacing is still ten to the inch, for which I profusely apologize to the rest of the world.
When that happens, the unit most commonly used for mechanical drawing is the inch. We'll go to hundreds of inches where necessary, and it's decimalized as needed. We never use fractions. In common American engineering slang, a "mil" is a thousandth of an inch.
American carpenters (really the whole building trade) still uses binary subdivision fractions of an inch, and still makes extensive use of primes notation. However, when the inches are subdivided, it's common to add a dash between the integral inches and the inch fragment. This helps especially when dimensions are written by hand.
So if you're going to use eighths of an inch and primes notation, the correct version would be 6′ 2-⅛″, read "six feet, two and one-eighth inches." And you would put a zero in the integrals place before the dash: 3′ 0-½″.
What you've written above, as JesseCuster pointed out, is actually:
6 feet, 2 feet, ⅛ inch (which equates to 8 feet, ⅛ inch)
Not really. It would more accurate to say what she wrote simply doesn't make sense. There's really no right way to read wrong notation.
