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A rational number is a number that can be expressed as a fraction.

This means it can either be a terminating decimal or a recurring decimal.

A terminating decimal is a decimal that doesn't recur (repeat for ever).

A recurring decimal is a decimal that repeats a pattern of numbers after the decimal point.

A good example of this is 1/3. 1/3 = 0.333333.... it is a rational number

13.001001001 is a rational number. Either you meant it to recur or not it makes no difference.

13.001001001 = 13 + 1001001/1000000000 as a terminating decimal

13.001001001....... = 12988/999 as a recurring decimal

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Examples of numbers that are not rational:

sqrt(2), pi, exp

they are irrational as they cannot be expressed as fractions.

Q: Is 13.001001001 a rational or irrational number and why?

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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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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.

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

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