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A decimal is a rational number if it ever ends, or if it repeats

the same single digit or set of digits forever.

Q: How do you determine if a decimal is rational or not?

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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.

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

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

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.

Yes, all rational numbers can be written as decimal numbers.

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A repeating decimal is rational.

To change a fraction to the equivalent decimal:Divide the top number by the bottom number.Regarding rational / irrational:Not to worry. Every fraction that you can write with numbers is rational,and so the equivalent decimal is too, even if it never ends.

The decimal shows a repeating pattern. Repeating decimals are rational.

It is rational because it is a terminating decimal

Any terminating decimal is rational. So are repeating (periodic) decimals.Any terminating decimal is rational. So are repeating (periodic) decimals.Any terminating decimal is rational. So are repeating (periodic) decimals.Any terminating decimal is rational. So are repeating (periodic) decimals.

The decimal representation of a rational number.

You cannot. There is no way to determine if the number has or has not been rounded and so no way to determine if the number is a terminating, repeating or other form of decimal number. Without that information you cannot tell if it is rational.

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

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

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.

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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