Answer:
See Below.
Step-by-step explanation:
Let:
[tex]0.\overline{5}=n[/tex]
If we multiply both sides by 10, we get:
[tex]5.\overline{5}=10n[/tex]
Now, we will subtract n from both sides:
[tex]5.\overline{5}-n=10n-n[/tex]
On the left, we can replace the n:
[tex]5.\overline{5}-.\overline{5}=10n-n[/tex]
Subtract:
[tex]5=9n[/tex]
Divide both sides by 9:
[tex]n=\frac{5}{9}[/tex]
Hence:
[tex]n=0.\overline{5}=\frac{5}{9}[/tex]
