20211115, 07:53  #1 
"Matthew Anderson"
Dec 2010
Oregon, USA
10010010101_{2} Posts 
the scary fraction of one seventh
Okay, it is not that scary.
Some of us know that 1/7 can be represented as an infinite repeating decimal. The six digits are 1,4,2,8,5, and7 So here it is with those digits twice, because we all want to see it twice :) 1/7 = 0.142857 142857 Regards, Matt 
20211115, 09:04  #2 
"Καλός"
May 2018
5·73 Posts 
Here is a link to more fun facts about 142857, see https://en.wikipedia.org/wiki/142,857.

20211115, 09:14  #3 
"Oliver"
Sep 2017
Porta Westfalica, DE
2×11×53 Posts 
Edit: This first part is also seen on the page Dobri provided. I was slower with my writeup than he with a link. The arithmethic progression shown there based on 3 is also interesting.
You can also see how \[\frac{1}{7}=\sum^{\infty}_{n=1}{\frac{2^n\cdot{}7}{10^{2n}}}\] by "visually inspecting" the terms: Code:
x  value of xth term  1  0.1400000000 2  0.0028000000 3  0.0000560000 4  0.0000011200 5  0.0000000224 ...  = 0.142857142... This latter one can be generalised: For \(\frac{1}{89}\), we have "one digit per \(F_n\)". If you want to have \(d\) digits, you should take \[\frac{1}{10^{2d}10^d1}=\sum^{\infty}_{n=0}{\frac{F_n}{10^{d\cdot{}n+1}}}\] instead, e.g. \(d=4\): \[\frac{1}{10^{2d}10^d1}=\frac{1}{10^810^41}=\frac{1}{99989999}=0.\ 0000\ 0001\ 0001\ 0002\ 0003\ 0005\ 0008\ 0013\ 0021\ 0034\ 0055\ 0089\ 0144 \dots\] Last fiddled with by kruoli on 20211115 at 09:20 Reason: Crosspost. 
20211125, 03:49  #4 
"Matthew Anderson"
Dec 2010
Oregon, USA
3·17·23 Posts 
The two previous posts are very cool.

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