Let us find if decimal numbers are rational or irrational
Let us look at some examples
Q: Is 2.5 a rational number?
-a-
Since 2.5 has a terminating expansion
So, it is a rational number.
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Q: Is 0.142857142… a rational number?
-a-
0.142857142… = 0.1428571428570142857…
Since the terminal expansion is non- terminating repeating.
It is a rational number.
-ea-
Q: Is 1.10100100010000.. a rational number?
-a-
1.10100100010000..
Since the terminal expansion is non- terminating non-repeating.
It is an irrational number.
-ea-