Reciprocal of 11
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Theorem
The decimal expansion of the reciprocal of $11$ is as follows:
- $\dfrac 1 {11} = 0 \cdotp \dot 0 \dot 9$
This sequence is A010680 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.0909... ------------ 11)1.000000000 99 ---- 100 99 --- ...
$\blacksquare$