Answer:
[tex] \frac{83}{99}[/tex]
Step-by-step explanation:5
We have to expressed the [tex]0.\overline{83}[/tex] as a fraction in simplest form.
Let x = [tex]0.\overline{83}[/tex] = 0.8383... ....[1]
Multiply by 100 to both sides we have;
[tex]100x = 83.8383..[/tex] ....[2]
Subtract [1] from [2] we have;
[tex]99x = 83[/tex]
Divide both sides by 99 we have;
[tex]x = \frac{83}{99}[/tex]
Therefore, the [tex]0.\overline{83}[/tex] as a fraction in simplest form is, [tex] \frac{83}{99}[/tex]
