Reciprocal of 101
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Theorem
The decimal expansion of the reciprocal of $101$ is as follows:
- $\dfrac 1 {101} = 0 \cdotp \dot 009 \dot 9$
This sequence is A021105 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.00990099... -------------- 101)1.00000000... 909 --- 910 909 --- 1000 909 ---- 910 909 --- ...
$\blacksquare$