Any number that you can completely write down on paper is rational.
You wrote (or typed) 67. Therefore it's rational.
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Rational.
Yes. 67/100 is a ratio (fraction) Since it can be put into a ratio, it is a rational number.
Yes.
An irrational number.
You can divide 65 by rationals and irrationals: Divided by a rational: 65 ÷ 13/2 = 10 Divided by an irrational: 65 ÷ √13 = 5√13