Is -6 Irrational Or Rational

The key divergence between rational and irrational numbers is, the rational number is expressed in the class of p/q whereas it is not possible for irrational number (though both are real numbers). Learn the definitions, more differences and examples based on them.

Definition of Rational and Irrational Numbers

Rational Numbers: The real numbers which can be represented in the class of the ratio of two integers, say P/Q, where Q is not equal to naught are called rational numbers.

Irrational Numbers: The real numbers which cannot exist expressed in the form of the ratio of ii integers are called irrational numbers.

What is the Deviation Between Rational Numbers and Irrational Numbers?

Southward.No	Rational Numbers	Irrational Numbers
1	Numbers that can be expressed as a ratio of two numbers (p/q class) are rational numbers.	Numbers that cannot be expressed equally a ratio of two numbers are irrational numbers.
2	The decimal expansion of rational numbers is either terminating or recurring.	The decimal expansion of irrational numbers is not-terminating and non-recurring.
3	Rational numbers include perfect squares such every bit 4, ix, 16, 25, and and so on.	Irrational numbers include surds such as √two, √iii, √5, √7 then on.
iv	Both the numerator and denominator are integers, in which the denominator is not equal to aught.	Irrational numbers cannot be written in fractional class.
5	Example: 3/2 = ane.v, 3.6767	Example: √5, √11

Video Lesson on Rational Numbers

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Oftentimes Asked Questions – FAQs

What is the main departure between rational and irrational numbers?

We tin can stand for rational numbers in the course of the ratio of two integers(positive or negative), where the denominator is not equal to 0. But nosotros cannot express irrational numbers in the same grade.

Give examples of rational and irrational numbers.

Examples of rational numbers are ane/ii, iii/four, 11/ii, 0.45, 10, etc.
The examples of irrational numbers are Pi (π) = 3.14159…., Euler's Number (e) = (2.71828…), and √3, √2.

How tin we place if a number is rational or irrational?

If a number has a terminating or repeating decimal, information technology is rational; for case, 1/2 = 0.five.
If a number has a not-terminating and not-repeating decimal, information technology is irrational, for example, o.31545673…

Is 2/3 rational or irrational?

2/3 = 0.66666…
Nosotros can meet, after simplification, two/iii is a repeating decimal. Hence, it is a rational number.