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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।

MathematicsA student says that if the decimal expansion of a number is non-terminating and non-repeating, then the number is irrational. What is the correct analysis of this statement?Class 9Number SystemsReal NumbersHard MathematicsWhat type of decimal expansion does the simplified form of 126/224 have?Class 9Number SystemsDecimal representationHard MathematicsWhat will be the decimal expansion of the simplified form of ( \frac{96}{384} )?Class 9Number SystemsReal NumbersHard MathematicsIf \(p/q\) is a rational number, where \(p\) and \(q\) are coprime integers and \(q>0\), which statement about its decimal expansion is correct?Class 9Number SystemsReal NumbersHard MathematicsWhich of the following numbers has a non-terminating, non-recurring decimal expansion?Class 9Number SystemsReal NumbersHard MathematicsA student says that the number \(0.101001000100001\ldots\) is rational because the digit 1 occurs repeatedly. The number of zeros before each successive 1 keeps increasing. Which is the correct evaluation of the student's statement?Class 9Number SystemsReal NumbersHard MathematicsA student says that 0.101001000100001… is a rational number because it contains only the digits 0 and 1. Which is the correct evaluation of the student's statement?Class 9Number SystemsReal NumbersHard MathematicsWhich of the following conditions about the decimal expansion of a real number definitely identifies it as irrational?Class 9Number SystemsReal NumbersHard MathematicsA student says that \(0.1010010001\ldots\) is a rational number because it contains only the digits 0 and 1. Why is the student's statement incorrect?Class 9Number SystemsReal NumbersHard 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 NumbersHard MathematicsWhich of the following numbers has a non-terminating recurring decimal expansion?Class 9Number SystemsReal NumbersHard MathematicsWhat is the decimal expansion of the simplified form of \(\frac{22}{77}\)?Class 9Number SystemsReal NumbersHard MathematicsWhat will be the decimal expansion of the simplified form of ( \frac{39}{312} )?Class 9Number SystemsReal NumbersHard MathematicsIf the decimal expansion of a real number is non-terminating and non-recurring, what type of number is it?Class 9Number SystemsReal NumbersHard MathematicsWhich of the following numbers is irrational because its decimal expansion is non-terminating and non-repeating?Class 9Number SystemsReal NumbersHard 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 NumbersHard 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 NumbersHard 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 NumbersMedium 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 NumbersMedium 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 NumbersMedium