Mathematics
Irrational numbers
अपरिमेय संख्याएँ
In this Class 9 Mathematics topic from the Number Systems chapter, students learn that irrational numbers cannot be written in the form p/q, where p and q are integers and q is not zero. They explore familiar examples such as √2 and π, understand their non-terminating, non-repeating decimal expansions, and distinguish them from rational numbers. The topic also develops skills for representing irrational numbers on the number line and understanding their place within the real number system.
Practice questions
Which of these numbers is not irrational?EasyLevel 17How is the decimal (0.123456789101112\ldots) considered?EasyLevel 17Riya says that \(0.101001000100001\ldots\) is a rational number because its decimal expansion does not terminate. Which is the correct evaluation of Riya’s statement?EasyLevel 17A student claims that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. What is the correct correction?EasyLevel 17A student says that \(0.101001000100001\ldots\) is a rational number because its decimal expansion never terminates. Which statement correctly identifies the student's error?EasyLevel 17What type of number is 3.14?EasyLevel 17Meena says that every non-terminating decimal is irrational. Which example proves her statement wrong?EasyLevel 17A student claims that every number with a non-terminating decimal expansion is irrational. Which of the following examples disproves the claim?EasyLevel 17Riya says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. What is the correct evaluation of Riya’s statement?EasyLevel 17Ravi wrote that \(0.101001000100001\ldots\) is a rational number because its digits follow an increasing pattern. What is the correct correction to Ravi’s statement?EasyLevel 17What is the value of \(\left(\frac{\sqrt{12}}{\sqrt{3}}\right)\)?EasyLevel 17Reema says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. Which statement correctly explains her error?EasyLevel 17What type of number is (1+\sqrt{2})?EasyLevel 17Which is an example of a non-terminating non-repeating decimal?EasyLevel 17Riya states, “The sum of any two irrational numbers is always irrational.” Which example proves her statement wrong?EasyLevel 17Between (\sqrt{64}) and (\sqrt{65}), which number is irrational?EasyLevel 17Which option is a correct example of an irrational number?EasyLevel 17Which part causes irrationality in (4√3)?EasyLevel 17What type of number is \((\sqrt{81}+\sqrt{2})\)?EasyLevel 17What is the simplified form of (√27 − √12)?EasyLevel 17