It is rational, since it can be written as one whole number divided by another whole number. For example, it can be written as:
3122333444455555/1000000000000000. A somewhat laborious way to write a number, but it can be done.
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10.01 is a rational number
Rational
Such a product is always irrational - unless the rational number happens to be zero.
The sum of a rational and irrational number must be an irrational number.
rational * irrational = irrational.