Respuesta :
0.482 repeat 82=(4.82 repeat 82)/10=(4+82/99)/10=(478/99)/10=478/990
The trick is that 0.82 repeat 82 =82/99
The trick is that 0.82 repeat 82 =82/99
Answer:
[tex]0.4\bar{82}=\frac{239}{495}[/tex]
Step-by-step explanation:
Given : Expression 0.482 repeating as a fraction with only the 82 repeating.
To find : What is expression as a fraction?
Solution :
Expression is given by, [tex]0.4\bar{82}[/tex]
Let [tex]x=0.4828282...[/tex] ....(1)
Multiply both side by 100,
[tex]100x=48.2828282...[/tex] .....(2)
Subtract (1) and (2),
[tex]100x-x=(48.2828282....)-(0.4828282...)[/tex]
[tex]99x=47.8[/tex]
[tex]x=\frac{47.8}{99}[/tex]
[tex]x=\frac{478}{990}[/tex]
[tex]x=\frac{239}{495}[/tex]
Therefore, [tex]0.4\bar{82}=\frac{239}{495}[/tex]
