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June 7th, 2014, 05:25 AM  #1 
Newbie Joined: Apr 2014 From: USA Posts: 24 Thanks: 1  rational number
Can you give me an example of an infinite decimal RATIONAL number formed by natural numbers used just once? It should be of the form ( 0,..............) . 
June 7th, 2014, 05:42 AM  #2 
Senior Member Joined: Apr 2014 From: zagreb, croatia Posts: 234 Thanks: 33 Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology 
0,3333333

June 7th, 2014, 01:25 PM  #3 
Newbie Joined: Jun 2014 From: Princeton wv Posts: 4 Thanks: 0  What am I missing?
Definition: " a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero." Wy does 1/3 not qualify? 
June 7th, 2014, 02:08 PM  #4 
Senior Member Joined: Apr 2014 From: zagreb, croatia Posts: 234 Thanks: 33 Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology  
June 7th, 2014, 05:42 PM  #5 
Member Joined: Feb 2012 From: Hastings, England Posts: 83 Thanks: 14 Math Focus: Problem Solving 
there's quite a few surely, 1/9 is another?

June 7th, 2014, 08:22 PM  #6 
Senior Member Joined: Apr 2014 From: zagreb, croatia Posts: 234 Thanks: 33 Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology  
June 8th, 2014, 04:31 PM  #7  
Global Moderator Joined: May 2007 Posts: 6,684 Thanks: 659  Quote:
All the answers are for one digit repeated. There are 8 possibilities: 0.nnnnnn........ = n/9 where n is any integer from 1 to 8.  
June 8th, 2014, 06:53 PM  #8 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,600 Thanks: 2588 Math Focus: Mainly analysis and algebra 
I wondered whether it was a request for an infinite decimal expansion in which no natural number is repeated. But any infinite decimal expansion of a rational will do. For example $\frac13 = 0.3\,33\,333\,3333\,33333\,\cdots$ where the spaces are inserted to highlight the natural numbers used. 
June 9th, 2014, 06:33 AM  #9  
Newbie Joined: Apr 2014 From: USA Posts: 24 Thanks: 1  Quote:
But it must respect a rule.  
June 9th, 2014, 06:33 AM  #10 
Newbie Joined: Apr 2014 From: USA Posts: 24 Thanks: 1  

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