Given:
The number is [tex]3.\overline{5}[/tex].
To find:
The simple fraction of the given number.
Solution:
Let us assume,
[tex]x=3.\overline{5}[/tex]
Then,
[tex]x=3.555...[/tex] ...(i)
Multiply both sides by 10.
[tex]10x=35.555...[/tex] ...(ii)
Subtracting (i) from (ii), we get
[tex]10x-x=35.555...-3.555...[/tex]
[tex]9x=32[/tex]
[tex]x=\dfrac{32}{9}[/tex]
Therefore, the simplified fraction form of the given number is [tex]\dfrac{32}{9}[/tex].
