All rational numbers CAN be expressed as a ratio of two integers. They may appear, before simplification, to be expressed in other forms.
For example, the rational number 1 can be written as the ratio sin(45)/cos(45) even though neither numerator nor denominator is an integer.
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Rational numbers are integers and fractions
No, not all rational numbers are integers. All integers are whole numbers, but a non-whole number can be rational if the numbers after the decimal point either 1. end or 2. repeat. So, sometimes rational numbers are integers, sometimes they're not. But all integers are rational numbers.
All integers are rational numbers. As a result, there are no such numbers. There is, therefore, no name for these non-existent numbers.
A rational number is one that can be expressed as the ratio of two integers. All integers (which includes 51) are themselves rational numbers as they can be written 51 = 51/1
Rational numbers are numbers that can be expressed as the quotient of two integers (3/2, 15/16). All integers, then, are rational numbers (12 = 12/1).