It isn't always possible to determine. For example, it is unknown whether the Euler-Mascheroni constant (0.5772156649...) is rational or irrational.
Most famous numbers and constants are known to be rational or irrational. If it can be expressed as a fraction a/b where a and b are integers, it's rational.
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If it can't be expressed as a fraction then it is an irrational number
All whole numbers are rational. Any rational number divided by another (non-zero) rational number is a rational number.
Irrational.
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
It will be irrational.