They need not be. You can have sqrt(23)% which would be irrational.
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Because percentages can be expressed as fractions which are rational numbers
The answer will depend on whether you want percentage equivalents of rational numbers or one rational number as a percentage of another.
It is finding an equivalent number whose denominator is 100.
They are called rational numbers
It depends on the percentage. A 1 cm arc of a circle whose radius is 1 cm will represent 100*1/(2pi) % = 50/pi % and that is an irrational percentage. A semicircular arc of the same circle will represent 50%, which is rational.