Is $1.0000...$ ( $1$ with infinite zeros) greater than $1.0$? Given that $0.3333...$ is greater than $0.3$ and similarly $0.777...$ is greater than $0.7$, does it follow that the sum of $0.33...$ and $0.77...$ is greater than sum of $0.3$ and $0.7$? 

 0.3 = 0.300000...   
       0.333333... 

 0.3 < 0.33333...

 0.7 = 0.700000...   
       0.777777...

 0.7 < 0.77777...

   0.3   
 + 0.7
  ----
   1.0

   0.33333...
 + 0.77777...
   ------------
   1.11111....

 1.0 < 1.11111...

