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What is the difference between recurring and non recurring decimal?
A recurring decimal is a rational number, a non-recurring one may be rational (for example 0.2 = 1/5) or irrational.
Why decimal is considered as rational number?
A decimal need not be a rational. A non-terminating, non recurring decimal is an irrational number. Only a terminating decimal or a recurring decimal is rational and that is because such a number can be expressed as a ratio of two integers.
Is decimal a rational number?
It depends. A terminating decimal is a rational number. A decimal which, after a finite number of places, becomes a repeating (or recurrent) decimal is also a rational number. A decimal that is not terminating, nor [eventually] settles into a recurring pattern is not a rational number. Note that the decimal need not become recurring immediately.
Is 6.121231234. a rational number?
Yes, it is. Any terminating or a non-terminating recurring decimal is a rational number. In this case, the decimal is terminated. And so, this number is a rational number.
Is 3.245245245 a rational number?
Assuming that the number ends at that third 5, yes, the number is rational - as it has a defined end-point. If the number is equal to 3.245 recurring, then no, the number will not be rational.
