Rich:

Yours: "...-- I'm not sure I follow... you're sliding the ruler..."

That's okay if or when you are measuring the length of an existing item, and yes, it is ideal for discovering the closest fraction of measure. But...!
As I stated, the 15 divided/numbered digits have the number of divisions marked on the digit lower in position/number.
E.g. #1 is divided into "2" segments
#2-"3" segments, #3-"4", #4-"5", etc.

It would be ideal if the first unit were undivided, then each unit measure from the start position would correspond to the number of divisions.
#1-no lines "1", #2- one line "2" division, #3- two lines "3" divisions, etc.
Woops...I think I see what they were up to.

Each unit count corresponds to the number of times a digit is "divided" (how many lines used to divide the digit) ...not the number of divisions created by the lines.
5 lines divide a digit into 6 sections (1/6)...therefore it is situated in position #5 and the operator understands/realizes that it requires 1 line less to divide a segment into a given number of parts.
That sound logical, but, as with many aspects of their math, it's a variation or different point of view resulting in the same thing…I guess…!

Interesting note:
The drafting industry use a triangle shaped cross-sectional ruler with six (2 per side) various fractional divisions on one end and the same on the other (total 12 sets of fractions). Same application as the Rc and ideal for scaling drawings.

Best.
Clive