Question

What are irrational numbers? How do they differ from rational numbers? Give examples.

Answer 1

Hint: A rational number can be defined as the number which can be stated as the ratio of two numbers or which can be expressed as the p/q form or as the quotient or the fraction with non-zero denominator whereas, the numbers which are not represented as the rational are known as the irrational number.

Complete step-by-step answer:
Difference between the rational and irrational Numbers:
Rational numbers can be expressed in the form $ \dfrac{p}{q} $ whereas, the numbers which are not represented by $ \dfrac{p}{q} $ form are known as the irrational numbers.
In rational numbers, both the terms in the numerator and the denominator are whole numbers and the denominator can not be zero whereas the irrational numbers are not expressed in the form of the fraction.
Irrational numbers are non-terminating and non-repeating whereas the rational numbers can be terminating or the non-terminating.
For Example: $ \pi ,4.5213,\sqrt 7 $ are irrational numbers and
 $ 5,0.7,\dfrac{7}{8} $ are rational numbers.

Note: Remember the difference between the rational and the irrational number. The numbers which are not characterized as the rational are known as the irrational number. Always remember that between any two given numbers there are infinite rational and irrational numbers which is irrespective of how small or large the difference between the two numbers it may be. In irrational numbers, the numbers are in the form of decimal and are the non-repeating and non-terminating numbers.