37 is Second Number whose Period of Reciprocal is 3

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$37$ is the $2$nd positive integer (after $27$) the decimal expansion of whose reciprocal has a period of $3$:

$\dfrac 1 {37} = 0 \cdotp \dot 02 \dot 7$


From Reciprocal of $37$:

$\dfrac 1 {37} = 0 \cdotp \dot 02 \dot 7$

Counting the digits, it is seen that this has a period of recurrence of $3$.

It can be determined by inspection of all smaller integers that this is indeed the $2$nd to have a period of $3$.