Yes.
67/100 is a ratio (fraction)
Since it can be put into a ratio, it is a rational number.
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Rational.
Any number that you can completely write down on paper is rational. You wrote (or typed) 67. Therefore it's rational.
Yes and it is also a prime number
There is only one type of rational number, namely the type that follow the definition precisely: A rational number is a number that can be written as a fraction of two (relatively prime) whole numbers a and b. A number is either rational or not rational. 123/67 is a rational number. Pi, or the square root of six, are irrational numbers. In decimal form, a rational number has a finite amount of decimals, or a repeating pattern of them. An irrational number has infinitely many non-repeating decimals.
You can divide 65 by rationals and irrationals: Divided by a rational: 65 ÷ 13/2 = 10 Divided by an irrational: 65 ÷ √13 = 5√13