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Re: Is there a simple way to transform 1.1 to 11/10?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92976] Re: [mg92968] Is there a simple way to transform 1.1 to 11/10?
  • From: Jan Schmedes <jasch at crustal.ucsb.edu>
  • Date: Wed, 22 Oct 2008 05:35:42 -0400 (EDT)
  • References: <200810211024.GAA04964@smc.vnet.net>

If you use something like
rational[x_] = Round[Round[(x - Floor[x])^-1]*x]/Round[(x -  
Floor[x])^-1]

you get for
rational[1.0000001]
10000001/10000000

but for rational[1.0000000000001] you get
10007999171935/10007999171934

because 1.0000000000001-1 gives 9.99201*10^(-14) ...

Cheers

Jan
On Oct 21, 2008, at 3:24 AM, Alain Cochard wrote:

>
>
> The obvious
>
>    In[1]:= x=1.1`Infinity
>
> is not syntactically correct.
>
> I understand that SetPrecision[1.1,Infinity] does not work either:
>
>    In[3]:= SetPrecision[1.1,Infinity]
>
>            2476979795053773
>    Out[3]= ----------------
>            2251799813685248
>
>    In[4]:= N[%,20]
>
>    Out[4]= 1.1000000000000000888
>
> I searched the newsgroup and thought I had the solution with  
> Rationalize:
>
>    In[5]:= Rationalize[1.1,0]
>
>            11
>    Out[5]= --
>            10
>
> But
>
>    In[9]:= Rationalize[1.000000001,0]
>
>            999999918
>    Out[9]= ---------
>            999999917
>
>    In[10]:= N[%,20]
>
>    Out[10]= 1.0000000010000000830
>
> So any simple way?
>
> Thanks,
> Alain
>



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