Q: Why is a rational number either terminating or repeating?

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When expressed as a decimal, a rational number will either be terminating (end with a finite number of digits) or repeating (have a repeating pattern of digits).

It is either a terminating decimal or a repeating decimal.

That is the definition of a rational number.

Any rational number is either a repeating decimal, or a terminating 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.

Related questions

When expressed as a decimal, a rational number will either be terminating (end with a finite number of digits) or repeating (have a repeating pattern of digits).

It is either a terminating decimal or a repeating decimal.

That is the definition of a rational number.

Any rational number is either a repeating decimal, or a terminating 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.

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

If its decimal representation is either terminating or a repeating number then it is rational. Otherwise it is irrational.

Yes. Any terminating or non-terminating recurring decimal is a rational number.

No. A rational number is any terminating numeral. A repeating decimal is irrational.

Yes- every terminating or repeating decimal number is rational.

No, a rational number, expressed as decimal, is either a terminating decimal, such as 1/4 = 0.25, or a repeating decimal, such as 1/7 = 0.142857 142857 142857 ...

If a decimal number is terminating or non-terminating repeating then it can be represented as a rational number.0.333333333 = 333333333/1000000000 which is in the form of p/q - a rational number.