The Four Meanings of "Accurate to 3 Places"

[acapde]

I recently saw in the article’s forum a very interesting information from Joe Horn about decimal to fraction conversion and the meaning of “accuracy to n places” term. I had recently implemented fraction display for my RPN on HP39gs program (before I saw that post). I had used the PPC ROM algorithm with a slight modification.

I was comparing the results of my own implementation with the original PPC ROM DF routine (running on a 41 emulator) and the HP48G (→Q function).
If I store ‘3’ in R07 (41/PPC ROM) and use Fixed 3 display on HP48G I get the same result for SQRT(84): 999/109 (producing in fact an error slightly less than .0000138), not the expected 614/67 fraction (row 14) according to the article, I wonder why...

Additionally, I would like to play more with the continued fraction method. It seems that the implementation is not difficult but (being lazy) does anyone happen to have the algorithm already in (Sys) RPL / RPN or any other simple format?

Thank you / Best regards.

Andres

Joe’s article hyperlink: http://www.hpmuseum.org/forum/thread-9661.html