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Repeating fraction
If you convert the fraction 1/81 in a decimal number, it creates a pattern that repeats itself
The three points indicate that there are infinitely many decimal places.
Explanation
You can write this fraction as
We perform the calculation, and find
0 1 1 1 1 1 1 1 1 1 1 1 ... 0 1 1 1 1 1 1 1 1 1 1 ... 0 1 1 1 1 1 1 1 1 1 ... 0 1 1 1 1 1 1 1 1 ... 0 1 1 1 1 1 1 1 ... 0 1 1 1 1 1 1 ... 0 1 1 1 1 1 ... 0 1 1 1 1 ... 0 1 1 1 ... 0 1 1 ... 0 1 ... 0 ... ... _____________________________________________________________________ 0 . 0 1 2 3 4 5 6 7 8 9 (10) (11) (12) (13) (14) ...
The numbers greater than 9 are in parentheses. The number 0.0123456789(10)(11)(12) ... never stops, but always continues.
Note
This number is very similar to Champernowne's constant 0, 1 2 3 4 5 6 7 8 9 10 11 12 13 ... which is created by writing all the natural numbers in sequence.
HistoryThe bracketed writing method was developed by the French mathematician Augustin-Louis Cauchy (1789 - 1857). |