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June 7th, 2014, 05:25 AM   #1
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Question 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,..............) .
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June 7th, 2014, 05:42 AM   #2
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0,3333333
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June 7th, 2014, 01:25 PM   #3
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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?
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June 7th, 2014, 02:08 PM   #4
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Originally Posted by randyg45 View Post
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?
It does.
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June 7th, 2014, 05:42 PM   #5
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there's quite a few surely, 1/9 is another?
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June 7th, 2014, 08:22 PM   #6
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Originally Posted by nmenumber1 View Post
there's quite a few surely, 1/9 is another?
Yes. 0.11111111111111111111

2/3 = 0.66666666666
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June 8th, 2014, 04:31 PM   #7
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Quote:
Originally Posted by Roli View Post
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,..............) .
Did you mean using only one integer repeated or something else?

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.
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June 8th, 2014, 06:53 PM   #8
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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.
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June 9th, 2014, 06:33 AM   #9
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Quote:
Originally Posted by Roli View Post
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,..............) .
I think I wasn't clear. It should contain ALL the natural numbers ( as a bijection ) and each natural number should be used ONCE. It can go infinitely or not.
But it must respect a rule.
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June 9th, 2014, 06:33 AM   #10
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Originally Posted by raul21 View Post
It does.
I think I wasn't clear. It should contain ALL the natural numbers ( as a bijection ) and each natural number should be used ONCE. It can go infinitely or not.
But it must respect a rule.
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