Is a fraction a real number, rational number, irrational number ?

Question

Eli Assouline · Accepted Answer

A fraction of two integers is a rational number. It is also a real number.

Integers are the numbers: #0, 1, -1, 2, -2, 3, -3,...# Rational numbers are any number that can be expressed as #p/q# where #p# and #q# are integers and #q != 0#. So #5#, #12.42#, #-17/3# and #0# are rational numbers. There are infinitely many rational numbers, but they do not form a continuous line. The continuous line of numbers is called the real number line. It includes all the previous numbers we have mentioned, but also numbers like #sqrt(2)#, #pi# and #e#, which are not rational. Any real number that is not rational can be considered an irrational number.

Eli Assouline · Answer

undefined A fraction is a real number and can be either a rational number or an irrational number, depending on whether its decimal representation terminates or repeats (rational) or goes on forever without repeating (irrational).

Nathan Axel · Answer

undefined A fraction is a real number and can be either rational or irrational. If a fraction can be expressed as the quotient of two integers, where the denominator is not zero, then it is a rational number. Otherwise, if it cannot be expressed in this form, it is an irrational number.