If you want arithmetic to work perfectly, stick with rational numbers and extended precision integers.
The integer part of a ration number is <.x . The fractional part is 1|x. Thus: (<. , 1&|) 14r3 4 2r3 On Thu, Nov 13, 2014 at 1:47 PM, Linda Alvord <[email protected]> wrote: > In Grade 3 in USA students learn multiplication of numbers from 0 to 100, > (I'm not sure what happenes to division by zero). However they only deal > with fractions of single digit denominators. So having experiented a > little > with rationals, see my question at the end. > > N=:11 33333330575r99999991726 > $N > 2 > 6 2$N > 11 33333330575r99999991726 > 11 33333330575r99999991726 > 11 33333330575r99999991726 > 11 33333330575r99999991726 > 11 33333330575r99999991726 > 11 33333330575r99999991726 > > +/ 6 2$N > 66 99999991725r49999995863 > > +/ +/ 6 2$N > 3399999718683r49999995863 > > 3399999718683%49999995863 > 68 > > +/ 6#2r3 > 4 > +/ 7#2r3 > 14r3 > > In third grade the anser should be 4 2r3 or something like it. How are > rational fractions generally handled? > > Linda > > -----Original Message----- > From: [email protected] > [mailto:[email protected]] On Behalf Of Roger Hui > Sent: Thursday, November 13, 2014 10:58 AM > To: Beta forum > Subject: Re: [Jbeta] Odd Pattern of Rationals > > And, most importantly, > > x: 1%3 > 1r3 > > x: is subject to tolerance. The implementation can possibly be improved by > using the ideas in > > https://en.wikipedia.org/wiki/Continued_fraction#Best_rational_approximation > s > > > > On Thu, Nov 13, 2014 at 7:35 AM, Mike Day <[email protected]> > wrote: > > > FYI > > NB. enumerate x:0.333... for between 1 and 20 decimal places > > (>:i.20),.x:+/"1 (10^>:i.20)%~"1(3#~])"0>:i.q =. 20 > > > > 1 3r10 > > > > 2 33r100 > > > > 3 333r1000 > > > > 4 3333r10000 > > > > 5 33333r100000 > > > > 6 333333r1000000 > > > > 7 3333333r10000000 > > > > 8 1r3 > > > > 9 166666671r500000014 > > > > 10 3333333057r9999999173 > > > > 11 33333330575r99999991726 > > > > 12 1r3 > > > > 13 1r3 > > > > 14 1r3 > > > > 15 1r3 > > > > 16 1r3 > > > > 17 1r3 > > > > 18 1r3 > > > > 19 1r3 > > > > 20 1r3 > > > > > > in Windows 8 - same in J32 & J64 > > > > > > Mike > > > > > > On 13/11/2014 14:56, Ben Gorte - CITG wrote: > > > >> I guess that's why Linda asked: Should 0.33333333 really be 1r3 ? > >> Raul showed that it is. > >> > >> (I also don't get it) > >> ________________________________________ > >> From: [email protected] [beta-bounces@forums. > >> jsoftware.com] on behalf of Dan Bron [[email protected]] > >> Sent: Thursday, November 13, 2014 15:39 > >> To: [email protected] > >> Subject: Re: [Jbeta] Odd Pattern of Rationals > >> > >> Linda, exact numbers have to be exact from the get-go. If a number > >> starts out inexact, it will stay inexact forever, even if you later > apply > x: > >> (though then it will be quite exactly inexact :). > >> > >> Thus, to get 1r3 you must say 1r3. If you say 0.333 you'll get 0.333 . > >> That's not 1r3 and never will be. > >> > >> -Dan > >> > >> ----- Original Message --------------- > >> > >> Subject: [Jbeta] Odd Pattern of Rationals > >> From: "Linda Alvord" <[email protected]> > >> Date: Wed, 12 Nov 2014 23:10:14 -0500 > >> To: <[email protected]> > >> > >> Should 0.33333333 really be 1r3 ? > >> > >> > >> > >> x: 0.333333 > >> > >> 333333r1000000 > >> > >> x: 0.3333333 > >> > >> 3333333r10000000 > >> > >> x: 0.33333333 > >> > >> 1r3 > >> > >> x: 0.333333333 > >> > >> 166666671r500000014 > >> > >> x: 0.3333333333 > >> > >> 3333333057r9999999173 > >> > >> > >> > >> Linda > >> > >> > > > > --- > > This email is free from viruses and malware because avast! Antivirus > > protection is active. > > http://www.avast.com > > > > > > > > ----- > > No virus found in this message. > > Checked by AVG - www.avg.com > > Version: 2014.0.4765 / Virus Database: 4189/8565 - Release Date: > > 11/13/14 > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
