# 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 $101$:

$\dfrac 1 {101} = 0 \cdotp \dot 009 \dot 9$