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Irrational

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No.

The number can be represented by a terminating decimal so it is rational.

A number cannot be both rational and irrational. And unless you are into higher maths (and if you are, the distinction between rationals and irrationals will be child's play) there are none that are neither rational nor irrational. So, for your purposes, they must be one or the other but cannot be both.

Even if it is an infinite decimal, with 6868 going on for ever, it is rational.

Q: Is 0.686868 rational irrational both rational and irrational or neither rational nor irrational?

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No number can be both rational and irrational. And, at the level that you must be for you to need to ask that question, a number must be either rational or irrational (ie not neither). 0.555555 is rational.

If it ends there, it is rational. If the "68" continues on and on, it is also rational.

There is no such thing as a number that is both rational and irrational. By definition, every number is either rational or irrational.

Yes. A number can be either rational or irrational, but never both; otherwise there would be an inherent contradiction.

The set of real numbers is divided into rational and irrational numbers. The two subsets are disjoint and exhaustive. That is to say, there is no real number which is both rational and irrational. Also, any real number must be rational or irrational.

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Integers are rational. In the set of real numbers, every number is either rational or irrational; a number can't be both or neither.

No number can be both rational and irrational. And, at the level that you must be for you to need to ask that question, a number must be either rational or irrational (ie not neither). 0.555555 is rational.

If it can't be expressed as a fraction then it is an irrational number

It is rational.A number cannot be both rational and irrational.

Integers and fractions that have integers in the numerator and denominator are rational. A number can't be rational and irrational at the same time - irrational means "not rational".

0.727272 is the ratio of 727,272 and 1,000,000. So it's nice and rational.

If it ends there, it is rational. If the "68" continues on and on, it is also rational.

No, no number can be both rational and irrational.

No. A rational number is a number that either terminates or repeats. An irrational number neither terminates nor repeats. Therefore, it cannot be both.

It will be irrational.

It doesn't happen. A number cannot be both rational and irrational. It is possible for it to be NEITHER if it is not Real number, i.e. involves the square root of -1, i.e is an imaginary or complex number number.

It can't be both at the same time. Irrational means "not rational".