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17 December, 2017:

30 October, 2016:

(Comments by Al Zimmermann dt 04-05-2017 )

The decimal expansions for 1/27 and 1/37 are as shown above because 27 37 = 999.
Another example would be:
1/271 = .00369 00369 00369
1/369 = .00271 00271 00271
because 271 369 = 99999.

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25 October, 2006:

(Comments by Al Zimmermann dt 01-05-2017 )

This fraction contains Fibonacci numbers up to 3 digits in length.
This can be generalized as follows::
The fraction 1/(10^2n-10^n-1) contains Fibonacci numbers up to n digits in length.
If n = 3, the fraction is 1 / (1000000 1000 1) = 1/998999.
For n = 4, the fraction is 1/99989999 = .0000000100010002000300050008001300210034005500890144.
The n leading zeroes in the decimal expansion can be considered the 0th term in the Fibonacci series or they can be removed by changing the fractions numerator to 10^n:
10000/99989999 = .000100010002000300050008001300210034005500890144.

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