Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: 1/3 partitioned expansion in different bases
Replies: 28   Last Post: Feb 3, 2013 11:57 PM

 Messages: [ Previous | Next ]
 JT Posts: 1,434 Registered: 4/7/12
Re: 1/3 partitioned expansion in different bases
Posted: Feb 3, 2013 12:34 AM

On 2 Feb, 13:45, JT <jonas.thornv...@gmail.com> wrote:
> On 2 Feb, 13:40, JT <jonas.thornv...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On 2 Feb, 13:31, JT <jonas.thornv...@gmail.com> wrote:
>
> > > On 2 Feb, 13:18, JT <jonas.thornv...@gmail.com> wrote:
>
> > > > On 2 Feb, 08:47, JT <jonas.thornv...@gmail.com> wrote:
>
> > > > > On 2 Feb, 08:31, JT <jonas.thornv...@gmail.com> wrote:
>
> > > > > > On 2 Feb, 07:41, JT <jonas.thornv...@gmail.com> wrote:
>
> > > > > > > On 2 Feb, 07:07, JT <jonas.thornv...@gmail.com> wrote:
>
> > > > > > > > On 2 Feb, 06:45, JT <jonas.thornv...@gmail.com> wrote:
>
> > > > > > > > > On 1 Feb, 15:06, Frederick Williams <freddywilli...@btinternet.com>
> > > > > > > > > wrote:

>
> > > > > > > > > > JT wrote:
> > > > > > > > > > > And 0.999... would be expressed as 0.3 or.......?
>
> > > > > > > > > > What are you asking?  Does 0.9 recurring (in base 10)  have the same
> > > > > > > > > > value as 0.3 (in base 3)?  No, 0.9 recurring (in base 10) has the same
> > > > > > > > > > value as 1.0 (in base 3).

>
> > > > > > > > > > --
> > > > > > > > > > When a true genius appears in the world, you may know him by
> > > > > > > > > > this sign, that the dunces are all in confederacy against him.
> > > > > > > > > > Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

>
> > > > > > > > > Well actually in this numbersystem in base 3
> > > > > > > > > 0,3=1
> > > > > > > > > This means that 0,3 actually completes 0.999... in standard digit
> > > > > > > > > expansion, it is the sum of all possible fractions of a single natural
> > > > > > > > > number.

>
> > > > > > > > > So in my bases a single natural actually equals the sum of all
> > > > > > > > > fractions thus 1=0,3 in base 3 the decimal expansion is complete.

>
> > > > > > > > In reality though you will never use it since 3/3 equals one.
>
> > > > > > > Base 3
> > > > > > > In fact 1,3=2
> > > > > > > You may find funny, but it is not that strange, the fractions have
> > > > > > > completness, but of course in reality you never write 1,3 you write 2.

>
> > > > > > Well my next post will be the new numbersystem bases as a working
> > > > > > program for all bases, without.
> > > > > > For great justice remove all Zeroshttp://www.youtube.com/watch?v=3TQbDz6-4eM

>
> > > > > Well not this but next ;Fhttp://www.youtube.com/watch?v=Dqm4dQv4F9w
>
>
> > > As everyone knows cool cats where shades, and it prevents them from
> > > get full of holes, NyaN completed.

>
> > Did you know that Nya N means New N in swedish?
>
> 27,28,29 anal exams, i have no idea if you passed.

Fixed prezeros for the fractional digit parts, now to new Naturals
conversion.

<META http-equiv=Content-Type content="text/html;
charset=windows-1252">
<SCRIPT language=Javascript>
function anybase() {

fullnumber=document.doit.dnumb.value;
twoparts = fullnumber.split(",");
bas=document.doit.bval.value;

for(j=0;j<2;j++){
btwo=1;
bnr=0;
unr=0;
empty=0;
decimalnumber=twoparts[j];

k=0;
emtpy=0;
basestring="";
while(decimalnumber[k]==0){
empty++;
k++;
}
basestring=empty+",";

while (btwo<decimalnumber){
btwo=btwo*bas;
bnr++
}

while (decimalnumber>0){
unr++;
set=0;
for(i=bas;i>0;i--){
st=btwo*i;
if (decimalnumber>=st) {
decimalnumber=decimalnumber-st;
set=1;
basestring=basestring+i+",";
}
}
if(set==0 && decimalnumber!=0)basestring=basestring+0+",";
btwo=btwo/bas;
}
while (bnr>=unr){
basestring=basestring+0+",";
unr++;
}

}

controldec=document.doit.fracted.value;
show=document.doit.dnumb.value+"=";
//Control Radix by go back to decimal
darr = control.split(",");
decarr = controldec.split(",");
prezero="";
prezero=decarr[0];
document.doit.trash.value=prezero;

darr.reverse();
decarr.reverse();

total=0;
totalfrac=0;
multiple=1
for (i=1;i<darr.length;i++){
cval=darr[i];
cval=cval*multiple;
total=total+cval;
show=show+"("+multiple+"*"+darr[i]+")+";
multiple=bas*multiple;
}
pre="";
for (i=0;i<prezero;i++){
pre="0"+pre;
}
multiple=1
for (i=1;i<decarr.length-1;i++){
cval=decarr[i];
cval=cval*multiple;
totalfrac=totalfrac+cval;
show=show+"("+multiple+"*"+decarr[i]+")+";
multiple=bas*multiple;
}
totalfrac=pre+totalfrac;
totalfull=total+","+totalfrac;
document.doit.controlout.value=totalfull;
document.doit.overview.value=show;
}

</SCRIPT>
<HTML><BODY>
<FORM NAME=doit onSubmit="anybase(); return false;">
CHANGE BASE:
<input type=submit value="GO!"><P>
DECIMAL VALUE:<TEXTAREA NAME=dnumb COLS=30
ROWS=1>777777777777,3333333</TEXTAREA><BR>
BASE:<TEXTAREA NAME=bval COLS=30
ROWS=1>333</TEXTAREA><BR>
First Digit in Radix and Fraction tells proceeding 0's not that
important for N but for fractional digit part.<BR>
ROWS=1></TEXTAREA><BR>
FRACTION OUT:<TEXTAREA NAME=fracted COLS=200
ROWS=1></TEXTAREA><BR>

BACK TO DECIMAL CONTROL CONVERSION->
<TEXTAREA NAME=controlout COLS=30
ROWS=1></TEXTAREA><BR>
ROWS=1></TEXTAREA><BR>
(Programmers)TRASHCAN<TEXTAREA NAME=trash COLS=200
ROWS=1></TEXTAREA><BR>
</FORM>
</BODY>
</HTML>

Date Subject Author
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 forbisgaryg@gmail.com
2/1/13 JT
2/1/13 forbisgaryg@gmail.com
2/1/13 JT
2/2/13 JT
2/1/13 Frederick Williams
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/3/13 JT
2/3/13 Virgil
2/3/13 JT