Best Answer

Such numbers can be written in the form of a ratio of two integers. In the first case as a ratio of an integer and a power of ten, and in the second case as a ratio of an integer and one less than a power of ten. Since the denominators in both cases are non-zero integers, these are rational numbers.

Examples:

0.356 = 356/1000

0.356356356... (repeating) = 356/999

In the first case the number of zeros after 1 is the number of digits after the decimal point. In the second case, the number of 9s is one fewer than the length of the repeating string.

Q: Are all terminated in repeating decimals rational numbers and why?

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Terminating and repeating decimals are rational numbers.

Yes.

Yes.

Yes. Rational numbers are numbers or decimals that repeat or terminate. Irrational numbers do not. For example π is an irrational number.

Yes, they will.

Related questions

All repeating decimals are rational numbers. Not all rational numbers are repeating decimals.

Terminating and repeating decimals are rational numbers.

Repeating decimals are ALWAYS rational numbers.

Yes.

Repeating decimals are rational numbers if there is a pattern, like 0.22222222. If it is not a pattern, like 0.568964329, it is an irrational number.

They will always be rational numbers.

Yes.

Yes.

Yes. Rational numbers are numbers or decimals that repeat or terminate. Irrational numbers do not. For example π is an irrational number.

No. Numbers with terminating or repeating decimals are rational.

YES

Yes, they will.