My Math Forum Infinite number such as 0.969696969696...

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 May 20th, 2015, 08:57 AM #1 Senior Member     Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus Infinite number such as 0.969696969696... I have a question. Is there a name for a number such as 0.96969696... I know that this is just a repeating decimal, but is there a more specific name? My friend called it a narcissistic number, but I am not sure this is right or not. What kind of operation could produce such a number as this?
 May 20th, 2015, 09:20 AM #2 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra It's called a recurring decimal.
 May 20th, 2015, 09:34 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,664 Thanks: 2644 Math Focus: Mainly analysis and algebra ${96 \over 99} = {32 \over 33}$, I think. All recurring numbers are rational. Narcissistic numbers are different. Last edited by v8archie; May 20th, 2015 at 09:37 AM.
 May 26th, 2015, 08:21 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 I suspect your friend was making a joke, based on the "69". Thanks from neelmodi
May 26th, 2015, 09:18 AM   #5
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Joined: Dec 2006
From: Lexington, MA

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Hello, Mr Davis 97!

Quote:
 Is there a name for a number such as 0.96969696... ? What kind of operation could produce such a number as this?

Yes, it is called a repeating decimal.

$\text{It comes from: }\,0.96\,\!\overline{96}\,=\,\frac{96}{99} \,=\,\frac{32}{33}$

$\text{Similarly: }\,0.189\,\!\overline{189} \:=\:\frac{189}{999} \:=\:\frac{7}{37}$

$\text{And: }\,0.285714\,\!\overline{285714} \:=\:\frac{285714}{999999} \:=\:\frac{2}{7}$

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