Respuesta :
Answer: Our required simplified fraction is [tex]\dfrac{5}{11}[/tex]
Step-by-step explanation:
Since we have given that
[tex]0.\bar{45}[/tex]
We need to find the simplified fraction.
[tex]Let\ x=0.\bar{45}=0.45454545.......-----------------------(1)[/tex]
Multiplying by 100 on both the sides, we get that
[tex]100x=45.4545454545.........---------------------(2)[/tex]
Subtracting (2) from (1), we get that
[tex]100x-x=45.454545........0.454545......\\\\99x=45\\\\x=\dfrac{45}{99}\\\\x=\dfrac{5}{11}[/tex]
Hence, our required simplified fraction is [tex]\dfrac{5}{11}[/tex]
