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Rational Numbers

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

MathematicsIf \(r\) is a rational number and \(x\) is an irrational number, which of the following will always be irrational?Class 9Number SystemsReal NumbersLevel 2Hard MathematicsA student claims that the sum of two irrational numbers is always irrational. Which of the following examples disproves the claim?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsWhich of the following conditions about the decimal expansion of a real number definitely identifies it as irrational?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsWhich of the following statements is not always true?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsReema claims that the decimal expansion of \(\frac{13}{120}\) will terminate because 120 has both 2 and 5 as factors. Which option correctly identifies the error in Reema’s statement?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsWhich of the following numbers has a non-terminating recurring decimal expansion?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsA student says that if the given denominator of a fraction has a prime factor other than 2 and 5, then its decimal expansion must be non-terminating. Which of the following fractions shows the error in this statement?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsIf \(x\) is an irrational number, which of the following statements is always true?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsA student says that the decimal expansion of \(\frac{77}{480}\) will terminate because the prime factors of 480 include 2 and 5. Which is the correct evaluation of the student's statement?Class 9Number SystemsReal NumbersLevel 1Hard MathematicsA student says, “A number with an infinite decimal expansion is always irrational.” Which of the following examples proves that the student's statement is incorrect?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsRiya says that the sum of any two irrational numbers is always irrational. Which of the following examples disproves her statement?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsA student says that the number 0.101001000100001... is rational because 0 occurs repeatedly in it. Which option is correct about this statement?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsA student says that the decimal expansion of \(\frac{13}{375}\) will terminate because its denominator has 5 as a factor. What is the correct correction to the student's statement?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsWhat type of decimal expansion does \(\frac{37}{54}\) have?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsWhat is the correct statement about the decimal form of 7/66?Class 9Number SystemsDecimal representationLevel 3Medium MathematicsWhat is the correct statement about the decimal form of 33/160?Class 9Number SystemsDecimal representationLevel 3Medium MathematicsWhat is the correct statement about the decimal form of 11/17?Class 9Number SystemsDecimal representationLevel 3Medium MathematicsWhat type of real number is 4.616161...?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsA student says that the sum of two irrational numbers is always irrational. Which of the following examples disproves the statement?Class 9Number SystemsReal NumbersLevel 3Medium MathematicsA student says that if the denominator of a fraction in simplest form has a prime factor other than 2 and 5, its decimal expansion is non-terminating recurring. Which of the following fractions supports the student's statement?Class 9Number SystemsReal NumbersLevel 3Medium