Answer:
[tex]0.13\bar{6}[/tex] as fraction [tex]\dfrac{41}{300}[/tex]
Step-by-step explanation:
We are given a repeating decimal number.
[tex]0.13\bar{6}[/tex]
We need to change into fraction.
Repeating decimal means number repeat infinite number of times.
So, we can write [tex]0.13\bar{6}[/tex] = 0.1366666666..............
Let,
[tex]x=0.1366666666.......[/tex]
Multiply both sides by 100
[tex]100x=13.66666666.......-------------(1)[/tex]
Multiply both sides by 10
[tex]1000x=136.66666666......-------------(2)[/tex]
Subtract eq(2) - eq(1)
[tex]1000x-100x=136.666666.... - 13.666666....[/tex]
[tex]900x=123[/tex]
[tex]x=\dfrac{123}{900}=\dfrac{41}{300}[/tex]
Hence, [tex]0.13\bar{6}[/tex] as fraction [tex]\dfrac{41}{300}[/tex]
