The key difference in between rational and irrational numbers is, the rational number is expressed in the develop of p/q whereas it is not possible for irrational number (though both are real numbers). Find Out the meanings, even more differences and also examples based upon them.

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Definition of Rational and Irrational Numbers

Rational Numbers: The actual numbers which have the right to be stood for in the create of the ratio of 2 integers, say P/Q, wbelow Q is not equal to zero are called rational numbers.

Irrational Numbers: The genuine numbers which cannot be expressed in the create of the ratio of two integers are dubbed irrational numbers.

What is the Difference Between Rational Numbers and also Irrational Numbers?


S.NoRational NumbersIrrational Numbers
1Numbers that have the right to be expressed as a ratio of two number (p/q form) are termed as a rational number.Numbers that cannot be expressed as a proportion of 2 numbers are termed as an irrational number.
2Rational Number includes numbers, which are finite or are recurring in nature.These consist of numbers, which are non-terminating and also non-repeating in nature.
3Rational Numbers contains perfect squares such as 4, 9, 16, 25, and also so onIrrational Numbers consists of surds such as √2, √3, √5, √7 and also so on.
4Both the numerator and denominator are whole numbers, in which the denominator is not equal to zero.Irrational numbers cannot be composed in fractional create.
5Example: 3/2 = 1.5, 3.6767Example: √5, √11

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We deserve to reexisting rational numbers in the form of proportion of two integers(positive or negative), wbelow denominator is not equal to 0. But we cannot express irrational numbers in the same form.
The examples of rational numbers are 1/2, 3/4, 11/2, 0.45, 10, and so on.The examples of irrational numbers are Pi (π) = 3.14159…., Euler’s Number (e) = (2.71828…), and √3, √2.

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If a number is terminating number or repeating decimal, then it is rational, for example, 1/2 = 0.5.If a number is non-terminating and non-repeating decimal, then it is irrational, for example, o.31545673…
2/3 = 0.66666…We can watch, after simplification, 2/3 is a repeating decimal. Hence, it is a rational number.

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