Step-by-step explanation:
Here we have , 0.7777…=7/9 . And using this fact we need to find show that
0.077777...=7/90 . Let's show this:
In the equation [tex]0.077777...=7/90[/tex] , Let's evaluate RHS :
⇒ [tex]0.077777[/tex]
⇒ [tex]\frac{0.77777}{10}[/tex]
But According to question , 0.7777…=7/9 , So
⇒ [tex]\frac{0.77777}{10}[/tex]
⇒ [tex]\frac{\frac{7}{9}}{10}[/tex]
⇒ [tex]\frac{7}{9} (\frac{1}{10} )[/tex]
⇒ [tex]\frac{7}{90}[/tex]
Since , RHS=LHS . Therefore, [tex]0.077777...=7/90[/tex] is proved using fact 0.7777…=7/9 .
