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If the rational number \(\frac{p}{q}\) is in lowest terms, which property of \(q\) guarantees that its decimal expansion terminates?

Answer and explanation

Correct answer: The prime factors of \(q\) are only 2 and/or 5

In lowest terms, a decimal terminates only when the denominator has prime factors 2 and/or 5. A factor such as 3 causes repetition. Exam tip: reduce the fraction before checking its denominator.

Related tags

Number SystemsDecimal RepresentationRational NumbersTerminating DecimalsPrime FactorsMathematicsClass 9 Mcq

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