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Are irrational numbers never rational numbers?
Yes, irrational numbers are never rational numbers because irrational numbers can't be expressed, by definition, as a fraction of two integers.
Is the quotient of two nonzero numbers never a rational number?
The quotient of two nonzero integers is the definition of a rational number. There are nonzero numbers other than integers (imaginary, rational non-integers) that the quotient of would not be a rational number. If the two nonzero numbers are rational themselves, then the quotient will be rational. (For example, 4 divided by 2 is 2: all of those numbers are rational).
Are irrational numbers always integers?
No. An irrational number is one that is not a rational number. A rational number is once that equals one integer divided by another. So an irrational number cannot be represented by one integer divided by another integer, so it cannot be an integer!
Are repeating decimals sometimes always or never rational numbers?
always
Is a fraction never a rational number?
Fractions where both the numerator and divisor are rational numbers are always rational numbers.
