any number (including fractions, square roots and Pi) that are not 0 and are not square roots of negative numbers.
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Yes, as long as the two nonzero numbers are themselves rational. (Since a rational number is any number that can be expressed as the quotient of two rational numbers, or any number that can be written as a fraction using only rational numbers.) If one of the nonzero numbers is not rational, the quotient will most likely be irrational.
The product of an irrational number and a rational number, both nonzero, is always irrational
A rational number is always the result of dividing an integer when the divisor is nonzero.
yes, as it can be expressed as the quotient of two (nonzero) integers (for example, 875 divided by 1000)
Then p/q is a rational number.