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Q: How can a decimal be a rational number-?

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Any decimal number that can be expressed as a fraction is a rational number

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

It is rational. An irrational number is a number that you cannot define by a fraction or a decimal. Since you wrote it as a decimal, it is rational.

No. It is a rational number. Any repeating decimal or terminating decimal is rational.

It is 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.

It is rational. An irrational number is a number that you cannot define by a fraction or a decimal. Since you wrote it as a decimal, it is rational.

Since 2.33333... is a repeating decimal (or recurring decimal), it is a rational number.

Decimals are real. They can be rational or irrational.

A number with a finite number of decimal digits is always rational. (If the number of decimal digits is infinite, the number is rational only if there is a repeating pattern.)

A decimal rational number can be expressed as a fraction A decimal irrational number can not be expressed as a fraction

The decimal representation of a rational number.

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