# Reciprocal of 7

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## Theorem

The decimal expansion of the reciprocal of $7$ has the maximum period, that is: $6$:

$\dfrac 1 {7} = 0 \cdotp \dot 14285 \, \dot 7$

## Proof

Performing the calculation using long division:

   0.142857...
------------
7)1.000000000
7
--
30
28
--
20
14
--
60
56
--
40
35
--
50
49
--
10
7
--
..


$\blacksquare$