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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।

MathematicsNidhi says that the number \(0.101001000100001\ldots\) is rational because its decimal expansion contains only 0 and 1. Which statement correctly explains Nidhi's error?Class 9Number SystemsIrrational numbersExpert MathematicsWhich of the following statements correctly identifies the decimal expansion of an irrational number?Class 9Number SystemsIrrational numbersExpert MathematicsWhich of the following statements is necessarily true for every irrational number \(x\)?Class 9Number SystemsIrrational numbersExpert MathematicsReema writes the number \(0.101001000100001\ldots\), in which the number of zeros between successive 1s keeps increasing. Which conclusion about this number is correct?Class 9Number SystemsIrrational numbersExpert MathematicsWhich of the following numbers, based on its decimal expansion, is irrational?Class 9Number SystemsIrrational numbersExpert MathematicsA student says, “Every number with a non-terminating decimal expansion is irrational.” Which of the following numbers proves this statement wrong?Class 9Number SystemsIrrational numbersExpert MathematicsA student says that every non-terminating decimal number is irrational. Which of the following numbers shows the error in this statement?Class 9Number SystemsIrrational numbersHard MathematicsA student claims that the number 0.101001000100001... is rational because it contains only the digits 0 and 1. What is the correct evaluation of this claim?Class 9Number SystemsIrrational numbersHard MathematicsWhich of the following decimal representations denotes an irrational number?Class 9Number SystemsIrrational numbersHard MathematicsA student examines the number \(x=0.101001000100001\ldots\) and draws a conclusion about its type. Which of the following conclusions is correct?Class 9Number SystemsIrrational numbersHard MathematicsA student says that the decimal number \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which statement correctly identifies the student's error?Class 9Number SystemsIrrational numbersMedium MathematicsWhich of the following numbers has a decimal expansion that indicates it is an irrational number?Class 9Number SystemsIrrational numbersMedium MathematicsA student claims that the number 0.101001000100001... is rational because it contains only the digits 0 and 1. Which statement correctly corrects the student's claim?Class 9Number SystemsIrrational numbersMedium MathematicsA student says that every non-terminating decimal expansion is irrational. Which of the following numbers disproves the statement?Class 9Number SystemsIrrational numbersMedium MathematicsA student says that every non-terminating decimal is irrational. Which example shows the error in this statement?Class 9Number SystemsIrrational numbersMedium MathematicsA student says, “Every non-terminating decimal expansion is irrational.” Which of the following examples proves this statement wrong?Class 9Number SystemsIrrational numbersMedium MathematicsRahul says that every number with an infinite decimal expansion is irrational. Which of the following examples proves Rahul’s statement wrong?Class 9Number SystemsIrrational numbersMedium MathematicsRiya says that the number \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1, and the number of zeros between successive 1s keeps increasing by one. What is the correct evaluation of Riya's statement?Class 9Number SystemsIrrational numbersMedium MathematicsReema says that every non-terminating decimal is an irrational number. Which of the following examples shows the error in her statement?Class 9Number SystemsIrrational numbersMedium MathematicsA student says that 0.101001000100001… is rational because it contains only the digits 0 and 1. What is the correct evaluation of this statement?Class 9Number SystemsIrrational numbersMedium