An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. A rational number can be.
2 is rational.
The square root of 2 is irrational.
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A rational number is one that can be expressed as a ratio of two integers: thus x = p/q where q is not zero. An irrational number cannot be expressed in such a way.
One consequence is that a rational number, in decimal form, is either a terminating decimal or an infinite recurring decimal. An irrational number has an infinite decimal from that is non-repeating.
Examples of rational numbers: 2, -3/4, -3.756, 18.23464646.. (recurring)
Examples of Irrational Numbers: sqrt(2), pi, phi (the Golden Ratio), e (Euler's number) as well as their negatives.
rational and irrational
-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.
Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Infinitely many. In fact, between any two different real numbers, there are infinitely many rational numbers, and infinitely many irrational numbers. (More precisely, beth-zero rational numbers, and beth-one irrational numbers - that is, there are more irrational numbers than rational numbers in any such interval.)
Directed numbers have a positive or negative sign associated with them. (The positive sign may be implied). They can be rational fractions (including mixed numbers) or irrational. Integers cannot be fractions or irrational.