Question

How do you convert `0.``dot4``dot7` to a fraction?

Answer 1

`47/99`

Explanation:

Let's take your value, `0.` `dot4` `dot7`, as a variable such that:
`r=0.` `dot4` `dot7`

Since the `47` infinityly repeats itself, we can easily cancel it:
If `r=0.` `dot4` `dot7`, then `100r=47.` `dot4` `dot7`

`99r=100r-r= 47.` `dot4` `dot7-0.` `dot4` `dot7` `=47`.

Now you have `99r=47`, divide both sides to find `r`:
`99r=47`
`r=47/99=0.` `dot4` `dot7`