Period : A decimal is called periodic with period $a_1a_2,\ldots,a_n$ if the sequence $a_1a_2,\ldots,a_n$ keeps on repeating forever in the decimal. For example $\frac{1}{3}=0.3333\ldots=0.\overline{3}$ has a period equal to 3. A function $f$ is called periodic with period $a$ if $f(x+a)=f(x)$ for all $x.$