rational vs real number

rational and real number both are nouns.

Word	Noun	Adjective	Verb	Adverb
rational	Yes	Yes	No	No
real number	Yes	No	No	No

As nouns, real number is a hypernym of rational; that is, real number is a word with a broader meaning than rational:

Other hypernyms of rational include real.

rational (noun)	real number (noun)
an integer or a fraction	any rational or irrational number

rational (adjective)	real number (adjective)
consistent with or based on or using reason
capable of being expressed as a quotient of integers
having its source in or being guided by the intellect (as distinguished from experience or emotion)
of or associated with or requiring the use of the mind