JT
Posts:
432
Registered:
4/7/12
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Re: 1/3 partitioned expansion in different bases
Posted:
Feb 1, 2013 12:49 AM
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On 1 Feb, 06:31, JT <jonas.thornv...@gmail.com> wrote:
> Sorry it was late night my head was not clear i try again.
>
> How is fraction 1/3 expressed in base 3, of course in base 10 it do
> have unfinished decimalexpansion.
> But has it really in base 3???
>
> And this is where number zero gets interesting, because when you use
> zero number 3 is expressed 10 in base 3 right?
>
> But in a number system without 0 it should *undoubtly* be expressed a
> single 3.
>
> And number 6 be 13 number 9 be 23 do you people agree?
> From this (may) also follow that 1/3 in such a number system would be
> expressed .1 do you people agree?
> And 0.999... would be expressed as 0.3 or.......?
>
> I could easily adjust my base changer to this, and in this zeroless
> number system 3+1/3 would be expressed 3,1
> 6+1/3 would be expressed 2,1
>
> Now can you people see any benefits from my new bases without 0. It
> seem that unfinished decimal expansion vanish in certain bases or?
>
> How does this basesystem make you feel angry, annoying or just
> uninteresting?
>
> Is there something deep profound to all this, if i just could
> remember
> what. I think it has something todo with factoring.
>
> For now i just wants commenting upon the proposed new bases without
> zeros good or bad, advantages disadvantages?
>
> Would you like me make a version of my base changer where 1/3 do not
> have unfinished decimal expansion and all bases expressed without
> zeroes?
Below is a standard base changer that change to anybase, with two or
three lines code we could finish the tyranny of unfinished decimal
expansion forever what do you say people shall we give it a go?
http://www.youtube.com/watch?v=qItugh-fFgg
<HTML><HEAD><TITLE>TEST</TITLE>
<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;
decimalnumber=twoparts[j];
while (btwo<decimalnumber){
btwo=btwo*bas;
bnr++
}
basestring="";
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++;
}
if (j==0) {radixout=basestring;document.doit.radix.value=radixout;}
if (j==1) {radixout=basestring;document.doit.fracted.value=radixout;}
}
control=document.doit.radix.value;
controldec=document.doit.fracted.value;
show=document.doit.dnumb.value+"=";
//Control Radix by go back to decimal
darr = control.split(",");
decarr = controldec.split(",");
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;
}
multiple=1
for (i=1;i<decarr.length;i++){
cval=decarr[i];
cval=cval*multiple;
totalfrac=totalfrac+cval;
show=show+"("+multiple+"*"+decarr[i]+")+";
multiple=bas*multiple;
}
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>
RADIX OUT:<TEXTAREA NAME=radix COLS=200
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>
Radix HOWTO EXPLAIN<TEXTAREA NAME=overview COLS=200
ROWS=1></TEXTAREA><BR>
</FORM>
</BODY>
</HTML>
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