Question

that 0.9999... is equal to 1

Answer 1

0.999..... = 0.9 bar
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let 0.9 bar = x
 
As there is only one digit under bar,

Now,

multiply by 10 on both sides,

10*0.9 bar = 10*x

9.9 bar = 10 x

subtract x from both sides,

 9.9 bar =10x
-0.9 bar = - x    

9 = 9x     [ bar will cancel ]

 Now,

x= 9/9 

x= 1

0.9 bar = 1


Hence,proved.


i hope this will help you


-by ABHAY