Answer:
[tex]\frac{5}{11}[/tex]
Step-by-step explanation:
The line over 45 indicates 45 is being repeated, that is
0.4545....
Create 2 equations with the repeating values after the decimal point
let x = 0.4545..... → (1) ( multiply both sides by 100 )
100x = 45.4545..... → (2)
Subtract (1) from (2) eliminating the repeating decimal
99x = 45 ( divide both sides by 99 )
x = [tex]\frac{45}{99}[/tex] = [tex]\frac{5}{11}[/tex]
Thus 0.4545... = [tex]\frac{5}{11}[/tex]
