Maths/Stats challenge - 1 of 2 - polls

[Joe Horn]

This class of question was addressed in a presentation at HHC 2012:
https://www.hpmuseum.org/forum/thread-7984.html
See "Chapter III: Fun application: Opinion Polls" in the PDF linked at the bottom of that posting.

Using the 50g's XQ function to answer this sort of problem was addressed here:
https://www.hpmuseum.org/forum/thread-7991.html

Here are some possibly non-obvious results for your suggested inputs (listed here in your posting's order):

Rounded to 1 significant digit:
10% --> 1/7
30% --> 1/3

Rounded to the number of significant digits indicated:
23% --> 3/13
23.0% --> 14/61 (*)
41% --> 7/17
41.0% --> 16/39
36% --> 4/11

12% --> 2/17
18% --> 2/11
45% --> 5/11 (*)

16% --> 3/19
02% --> 1/41 (*)
51% --> 18/35 (*)
51.0% --> 25/49
31% --> 4/13
31.0% --> 9/29
17% --> 1/6
17.0% --> 8/47
13% --> 1/8
13.0% --> 3/23

(*) -- these results are missed by the usual "continued fraction" method, but are found by brute search (slow) and by the PDQ algorithm (fast) as described by the above-linked article.