Reciprocal of 7
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Theorem
The decimal expansion of the reciprocal of $7$ is as follows:
- $\dfrac 1 7 = 0 \cdotp \dot 14285 \, \dot 7$
This sequence is A020806 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
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 -- ..
$\blacksquare$