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It is confusing, #8 32 x1/4 means 8 gauge ( diameter ), 32 teeth per inch, 1/4 inch long. Try not to worry about it too much, I forgot most of that crap 28 years ago when my apprenticeship finished :>).
I don't tip the scales on that many more years than you Rudi but I have worked on old Brit cars which means I have had to do the fractions before. I gave all my old imperial tools away as I ended up with all metric good stuff and then pinball came into my life.