Number times Recurring Part of Reciprocal gives 9-Repdigit/Mistake

Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary

$142,857$

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

The Dictionary

$142,857$

Mistake in First Edition

This is a property of all the periods of repeating decimals. If the period of $n$ is multiplied by $n$, the result is as many $9$s as there are digits in $n$.

Mistake in Second Edition

This is a property of all the periods of repeating decimals. If the period of $n$ is multiplied by $n$, the result is as many $9$s as there are digits in the period of $1/n$.