Question

How do you convert .444444444 to a fraction?

Answer 1

Assuming the decimal number has infinitely many digits, suppose


`x=0.444\ldots=0.\overline4`

Then


`10x=4.444\ldots=4.\overline4`

It follows that


`10x-x=4.\overline4-0.\overline4`

`\implies 9x=4`

`\implies x=\frac49`