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Mathematics

Only by inspecting the prime factors of the denominators, state which of the following fractions will be a recurring decimal?

  1. 716\dfrac{7}{16}

  2. 851\dfrac{8}{51}

  3. 325\dfrac{3}{25}

  4. 1120\dfrac{11}{20}

Rational Irrational Nos

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Answer

A rational number will have a recurring decimal expansion if and only if the prime factorization of its denominator contains any prime factor other than 2 or 5.

The prime factors of 51 are 17 and 3.

Hence, Option 2 is the correct option.

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