what is rational number and what is irrational number?

RATIONAL :

In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero.

Each rational number can be written in infinitely many forms, for example 3 / 6 = 2 / 4 = 1 / 2, but the simplest form is when a and b have no common divisors. Every non-zero rational number has exactly one simplest form of this type with a positive denominator. A fraction in this simplest form is said to be an irreducible fraction, or a fraction in reduced form.

The decimal expansion of a rational number is eventually periodic (in the case of a finite expansion the zeroes which implicitly follow it form the periodic part). The same is true for any other integral base above one, and is also true when rational numbers are considered to be p-adic numbers rather than real numbers. Conversely, if the expansion of a number for one base is periodic, it is periodic for all bases and the number is rational.

A real number which is not a rational number is called an irrational number.

In mathematics, an irrational number is any real number that is not a rational number, i.e., it cannot be expressed in the form

IRRATIONAL:


where a and b are integers and b is not equal to zero. It can readily be shown that the irrational numbers are precisely those numbers whose expansion in any given rational base (decimal, binary, etc) never ends and never enters a periodic pattern. Almost all real numbers are irrational, in a sense which is defined more precisely below.

When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable, meaning they share no measure in common. A measure of a line segment I in this sense is a line segment J that "measures" I in the sense that some whole number of copies of J laid end-to-end occupy the same length as I.

rational numbers Q, written in the simple form a/b where a and b are integers, without a common factor and b not equal 0

irrational numbers is a set of numbers like sq root of 2, which cannot be written in the form a/b where a and b are integers.

Rational number have an end of number.
Ex. 2, 5, 7,-2,0.24
irrational number is an endless number.
Ex. 0.1111... , 3.1452....