Let x = 0.191919...
Now, we want to find some sort of relationship with x and 0.191919...
If we multiply x by 100, we get:
[tex]100x = 19.19191919...[/tex]
Now, it's clear that the decimal places will cancel when we subtract it:
[tex]100x - x = 19.19191919... - 0.19191919...[/tex]
[tex]99x = 19[/tex]
Solving for x, we get:
[tex]x = \frac{19}{99}[/tex]
