Assuming the decimal number has infinitely many digits, suppose
[tex]x=0.444\ldots=0.\overline4[/tex]
Then
[tex]10x=4.444\ldots=4.\overline4[/tex]
It follows that
[tex]10x-x=4.\overline4-0.\overline4[/tex]
[tex]\implies 9x=4[/tex]
[tex]\implies x=\dfrac49[/tex]
