Reciprocal of 13
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Theorem
The decimal expansion of the reciprocal of $13$ is as follows:
- $\dfrac 1 {13} = 0 \cdotp \dot 07692 \dot 3 \ldots$
This sequence is A021017 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.07692307... ------------- 13)1.00000000... 91 ---- 90 78 -- 120 117 --- 30 26 -- 40 39 -- 100 91 --- ...
$\blacksquare$