Correct option is (a) True
The best I can explain: Let’s take a known rational number to understand this.
For example, 3/4
We know that 3/4 is a rational number because both 3 and 4 are natural
numbers and 3/4=0.75 which is terminating expansion.
Now, let’s take one example of non-terminating and recurring expansion.
For example 0.5787878…
Let x=0.5787878…
Then 100x=57.878787…
100x=57.3 + 0.5787878…
100x=57.3 + x
99x=57.3
Then, x=57.3/99
x=573/990
This is of the form of p/q where p and q are natural numbers. Hence we can say that .5787878… is rational number.
Hence, we can conclude that the decimal expansion of rational numbers is either terminating or non-terminating and recurring (repeating).
We can also conclude that ‘The decimal expansion of irrational numbers is non-terminating and non-recurring.’