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Decimal Expansion

Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsRima says, “\(\sqrt{2}\) is irrational because its decimal expansion is infinite.” What is the main flaw in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student says that the decimal expansion of \(\sqrt{3}\) is 1.732... and does not terminate; therefore, \(\sqrt{3}\) is irrational. What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA calculator displays \(\sqrt{3}\) as 1.7320508. Which conclusion is correct based on this display?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich of the following decimal expansions indicates an irrational number?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsRavi says that \(\sqrt{2}\) is irrational because its decimal expansion is infinite. What is the flaw in his argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsRiya says, “ \(\sqrt{3}=1.732\ldots\), so it is irrational because its decimal expansion is non-terminating.” What is the main error in Riya’s reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsRiya says that since a calculator displays \(\sqrt{2}\) as 1.414, \(\sqrt{2}\) is a rational number. What is the error in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsReema says, “The decimal expansion of \(\sqrt{3}\) is infinite, so it is irrational.” What is the flaw in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsA student says, “\(\sqrt{3}=1.732\), so \(\sqrt{3}\) is rational.” What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 21Easy MathematicsA student says that \(\sqrt{3}\) is rational because its value is approximately 1.73. Which comment about this statement is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says that \(\sqrt{3}\) is rational because 1.732 is a terminating decimal. What is the error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsRima says that if the decimal expansion of a number is infinite but non-repeating, then the number is rational. What is the error in Rima's statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsRiya says that \(\sqrt{2}\) is irrational because its decimal expansion never terminates. What is the flaw in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsRima says that \(\sqrt{2}\) is rational because its decimal form begins with 1.414.... What is the correct error in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student sees \(\sqrt{3}\) displayed as 1.732 on a calculator and claims that \(\sqrt{3}\) is rational because the decimal ends. Which statement correctly identifies the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsIn the number \(0.101001000100001\ldots\), the number of zeros between two successive 1s increases by one each time. A student says that it is rational because it contains only the digits 0 and 1. Which is the correct evaluation of the student's argument?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsA student calls the number 0.101001000100001… rational because it contains only the digits 0 and 1. Why is the student’s conclusion incorrect?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsWhich of the following decimal expansions definitely identifies the number as irrational?Class 9Number SystemsIrrational numbersLevel 15Expert MathematicsRiya claims that \(0.101001000100001\ldots\) is rational because only the digits 0 and 1 occur in it. Which is the correct refutation of her claim?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhich of the following decimal expansions identifies a real number as irrational?Class 9Number SystemsIrrational numbersLevel 14Expert