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
>>
>>
>
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