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Q: Is an irrational number always a non-repeating and non-terminating decimal number?

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No, it is not.

A decimal expansion means to write out the base 10 digits of a number. Because irrational numbers do not have a closed form, the decimal expansion will always be an approximation. Consider the irrational number pi, which has the following decimal expansion: 3.14159265... Of course there are more digits to pi than that, which is denoted by the "...". It is sadly impossible to list ALL of the digits of an irrational numbers, since if there were a finite number of digits, you could express it as a fraction, which would not be irrational.

Yes, always.

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.)

Yes.

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No, it is not.

No, that is false.

A decimal expansion means to write out the base 10 digits of a number. Because irrational numbers do not have a closed form, the decimal expansion will always be an approximation. Consider the irrational number pi, which has the following decimal expansion: 3.14159265... Of course there are more digits to pi than that, which is denoted by the "...". It is sadly impossible to list ALL of the digits of an irrational numbers, since if there were a finite number of digits, you could express it as a fraction, which would not be irrational.

Both rational and irrational numbers can be expressed with decimals. If the number is irrational, it will have an infinite number of decimal digits, and there will be no periodic repetition. For example, 1/7 (which is rational) is 0.142857 142857 142857... The same sequence of six digits repeats over and over again. In irrational numbers, this is not the case.

If the number of digits after the decimal point is finite, then the number will always be RATIONAL.

It is always irrational.

Yes, always.

No, it is always irrational.

Not always because any decimal that can be expressed as a fraction is a rational number as for example 0.33333.....repeating can be expressed as 1/3 which is a rational number

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.)

It is not always irrational.

Such a sum is always irrational.

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