Period of Reciprocal of 729 is 81/Mistake

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Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary
$729$


1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary
$729$


Mistake

$1 / 729$ has a decimal period of $81$ digits, which can be arranged in groups of $9$ digits, reading across each row, in this pattern:
\(\ds 001 \, 371 \, 742\) \(\) \(\ds \)
\(\ds 112 \, 482 \, 853\) \(\) \(\ds \)
\(\ds 223 \, 593 \, 964\) \(\) \(\ds \)
\(\ds 334 \, 705 \, 075\) \(\) \(\ds \)
\(\ds 445 \, 816 \, 186\) \(\) \(\ds \)
\(\ds 556 \, 927 \, 297\) \(\) \(\ds \)
\(\ds 668 \, \color {red} 6 38 \, 408\) \(\) \(\ds \)
\(\ds 779 \, 149 \, 519\) \(\) \(\ds \)
\(\ds 890 \, 260 \, 631\) \(\) \(\ds \)


The $\color { red } {\text {red} }$ digit is wrong.

Instead of $6$ it should be $0$:

\(\ds 001 \, 371 \, 742\) \(\) \(\ds \)
\(\ds 112 \, 482 \, 853\) \(\) \(\ds \)
\(\ds 223 \, 593 \, 964\) \(\) \(\ds \)
\(\ds 334 \, 705 \, 075\) \(\) \(\ds \)
\(\ds 445 \, 816 \, 186\) \(\) \(\ds \)
\(\ds 556 \, 927 \, 297\) \(\) \(\ds \)
\(\ds 668 \, \color {red} 0 38 \, 408\) \(\) \(\ds \)
\(\ds 779 \, 149 \, 519\) \(\) \(\ds \)
\(\ds 890 \, 260 \, 631\) \(\) \(\ds \)


Sources