Let us find if decimal numbers are rational or irrational

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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.

-ea-

**
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-