Answer:
[tex]0.\overline{23}= \frac{23}{99}[/tex]
Step-by-step explanation:
Let [tex]x = 0.\overline{23}[/tex]....(1)
Multiply both sides by 100.
[tex]100x = 23.\overline{23}[/tex]....(2)
Subtracting equation (1) from equation (2)
[tex]100x -x= 23.\overline{23}-0.\overline{23}[/tex]
[tex]\implies 99x= 23[/tex]
[tex]\implies x= \frac{23}{99}[/tex]
[tex]\implies\huge{\orange{ 0.\overline{23}= \frac{23}{99}}}[/tex]
