Answer:
The fraction form of given number is [tex]\frac{38}{111}[/tex].
Step-by-step explanation:
The given repeating decimal number is
[tex]0.\overline{342}[/tex]
Let [tex]x=0.\overline{342}[/tex]
It can be written as
[tex]x=0.342342342...[/tex]
The digits repeated after 3 decimal places. So multiply both sides by 1000.
[tex]1000x=0.342342342...\times 1000[/tex]
[tex]1000x=342.342342...[/tex]
[tex]1000x=342+0.342342...[/tex]
[tex]1000x=342+0.\overline{342}[/tex]
[tex]1000x=342+x[/tex]
Subtract x from both the sides.
[tex]1000x-x=342[/tex]
[tex]999x=342[/tex]
Divide both the sides by 999.
[tex]x=\frac{342}{999}[/tex]
[tex]0.\overline{342}=\frac{342}{999}[/tex]
Cancel out the common factors.
[tex]0.\overline{342}=\frac{38}{111}[/tex]
Therefore the fraction form of given number is [tex]\frac{38}{111}[/tex].
