Question

Is 1.111 .............. an irrational or a rational number? How can you prove it?

Answer 1

1.111...... is an rational number because it has non terminating repeating condition and it can be right in p/q form

i am proving below

let x = 1.1111.............(i) equation

and 10x = 11.1111............(ii) equation

subtracting equation (i) from equation (ii)


 10x = 11.1111.............
-    x =   1.1111.............
------------------------------
  9x  =  10.0000...........
 

9x = 10

x = 10/9

so 1.111 can be written in the form of p/q, so it is a rational number.