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A rational number terminates or repeats because in both cases they can be represented as a fraction (in a/b form.) When a number keeps going with no period (no part of the number repeats) it cannot be written in a/b form.

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Q: Why is a rational number a terminating or reapeting decimal?
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Related questions

What is non terminatin repeating decimal?

A terminating decimal is a rational number. A non-terminating, repeating decimal is a rational number. A non-terminating, non-repeating decimal is an irrational number.


Is 8.2 a rational number?

Yes. Any terminating decimal is a rational number. Any repeating decimal also.


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.


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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.


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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.


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