101 is Smallest Number whose Period of Reciprocal is 4

Theorem
$101$ is the first positive integer the decimal expansion of whose reciprocal has a period of $4$:
 * $\dfrac 1 {101} = 0 \cdotp \dot 009 \dot 9$

Proof
From Reciprocal of $101$:
 * $\dfrac 1 {101} = 0 \cdotp \dot 009 \dot 9$