Reciprocals of Prime Numbers

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Theorem

The deximal representations of the reciprocals of the first few prime numbers are as follows:

$n$ $1 / n$ Also see
$2$ $0 \cdotp 5$
$3$ $0 \cdotp \dot 3$
$5$ $0 \cdotp 2$
$7$ $0 \cdotp \dot 14285 \, \dot 7$ Period of Reciprocal of 7 is of Maximal Length
$11$ $0 \cdotp \dot 0 \dot 9$
$13$ $0 \cdotp \dot 07692 \dot 3$
$17$ $0 \cdotp \dot 05882 \, 35294 \, 11764 \, \dot 7$ Period of Reciprocal of 17 is of Maximal Length
$19$ $0 \cdotp \dot 05263 \, 15789 \, 47368 \, 42 \dot 1$ Period of Reciprocal of 19 is of Maximal Length
$23$ $0 \cdotp \dot 04347 \, 82608 \, 69565 \, 21739 \, 1 \dot 3$ Period of Reciprocal of 23 is of Maximal Length
$29$ $0 \cdotp \dot 3448 \, 27586 \, 20689 \, 65517 \, 24137 \, 93 \dot 1$
$31$ $0 \cdotp \dot 03225 \, 80645 \, 1612 \dot 9$ Period of Reciprocal of 31 is of Odd Length
$37$ $0 \cdotp \dot 02 \dot 7$ Period of Reciprocal of 37 has Length 3


Sources