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Q: Is .2020020002... a rational number or irrational number?

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It is a rational number.

It is a rational number

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.

Is 12.05 a rational number or irrational number?

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The answer depends on what the ellipsis represents. I suspect that the number is not rational.

If you mean that the number continues by a number of 0s which is one more than the previous numbers of 0s followed by a 2 forever, then it is an irrational number. If you mean that the "2020020002" repeats then it is a rational number.

10.01 is a rational number

It is a rational number.

Rational

It is a rational number

No rational number is an irrational number.

Irrational.

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

No number is irrational and rational.

Irrational. If you multiply a rational number by an irrational number, you will always get an irrational number (except if the rational number happens to be zero).

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

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