Q: Is 5.09090909 a rational number or irrational?

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Irrational.

The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.

No.A rational times an irrational is never rational. It is always irrational.

It will be irrational.

Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).

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10.01 is a rational number

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It is a rational number.

is 34.54 and irrational or rational. number

it is a rational number but 4.121314..... is an irrational no

Irrational.

Such a product is always irrational - unless the rational number happens to be zero.

The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.

No number is irrational and rational.

If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.

When a rational numbers is divided by an irrational number, the answer is irrational for every non-zero rational number.

The sum of a rational and irrational number must be an irrational number.