Correct option is (c) rational number
The explanation: Let 0.333…=x
Then, 10x=3.33333…
10x=3 + 0.333…
10x=3 + x
9x=3
Then, x=3/9=1/3
This is of the form p/q where p and q are natural numbers. Hence by definition, 0.3333…. is a rational number.
Another method: Decimal expansion of rational numbers is either terminating or non-terminating and recurring (repeating).
As we can see that 0.3333… is non-terminating and recurring so it is a rational number.