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Prime Factorisation

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

MathematicsWhich of the following rational numbers will have a non-terminating recurring decimal expansion?Class 9Number SystemsDecimal representationLevel 19Expert MathematicsRavi says that if, in simplest form, a fraction has only 2 and 5 as prime factors of its denominator, then its decimal expansion terminates. Which of the following fractions is an example supporting his statement?Class 9Number SystemsDecimal representationLevel 19Expert MathematicsWhich option is correct about the decimal expansion of \(\frac{13}{2^2\times5\times7}\)?Class 9Number SystemsDecimal representationLevel 19Expert MathematicsWhich of the following rational numbers has a terminating decimal expansion?Class 9Number SystemsDecimal representationLevel 19Expert MathematicsWhy is the decimal expansion of \(\frac{5}{6}\) not terminating?Class 9Number SystemsDecimal representationLevel 19Expert MathematicsIf p/q is a rational number and p and q are coprime, when will its decimal expansion terminate?Class 9Number SystemsDecimal representationLevel 19Expert MathematicsWhich of the following rational numbers will have a terminating decimal expansion?Class 9Number SystemsDecimal representationLevel 19Expert MathematicsWhich statement is correct about the decimal expansion of \(\frac{13}{40}\)?Class 9Number SystemsDecimal representationLevel 19Expert MathematicsIn the proof of √3, 3 | h² implies 3 | h. Which broader principle does this illustrate?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich of the following numbers can be proved irrational using its prime factorisation?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsIf (h) is not divisible by (3) and (h^2=3k^2), what inconsistency appears?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Expert MathematicsWhat problem appears when a² = 2b² is viewed through prime factors in the proof of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn a proof that \(\sqrt{3}\) is irrational, a student writes: “If \(3\mid p^2\), we can conclude only that \(p^2=3k\).” What is the correct correction needed to continue the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich idea about the exponents of prime factors explains the irrationality of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsFor a positive integer \(n\), which statement correctly identifies when \(\sqrt{n}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf a prime number has an odd exponent in the prime factorisation of a number, what can be concluded about the square root of that number?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich of the following rational numbers will have a terminating decimal expansion when written in its simplest form?Class 9Number SystemsDecimal representationLevel 12Expert MathematicsA student says that the decimal expansion of \(\frac{77}{480}\) will terminate because 480 is an even number. What is the student's error?Class 9Number SystemsDecimal representationLevel 12Expert MathematicsFor a rational number \(\frac{p}{q}\), where \(p\) and \(q\) are coprime, when will its decimal expansion be non-terminating recurring?Class 9Number SystemsDecimal representationLevel 10Expert MathematicsWhich of the following fractions will have a terminating decimal expansion even though its given denominator has 3 as a factor?Class 9Number SystemsDecimal representationLevel 10Expert