Ram Kushwah
Last Activity: 3 Years ago
Dear student ,
The decimal expansion of a real number can be of three types
1.Terminating
For exaple 0.125=1/8, 0.375=3/8,such numbers are always rational numbers
2.Non-terminating and repeating
Example : 0.333333...........=1/3
0.555555555555555555....=1/9
such numbers are also always rational numbers
2.Non-terminating and non-repeating
Example :
3.141592653589793.........................= ( irrational)
2.30300400050000.............................Irrational
such numbers are always irrational numbers
Now the given number is:
0.120120012000120000.......................................
Here we see that decimal expansion is not terminating( Not ending)
But here is not follwing any patter so it also nor repeating
Hence this number is non terminating and non repeating
Thus the number is AN IRRATIONAL NUMBER
