If x is a number whose simplest form is \(\frac {p}{q}\), where p and q are integers and q ≠ 0, then x is a non-terminating repeating decimal only when q is not of the form ________(a) 2^m×2^n(b) 5^m×5^n(c) 2^m×5^n(d) 3^m×4^nI had been asked this question in an international level competition.My question is taken from Irrational and Rational Numbers in division Real Numbers of Mathematics – Class 10

If x is a number whose simplest form is \(\frac {p}{q}\), where p and

1.	If x is a number whose simplest form is \(\frac {p}{q}\), where p and q are integers and q ≠ 0, then x is a non-terminating repeating decimal only when q is not of the form ________(a) 2^m×2^n(b) 5^m×5^n(c) 2^m×5^n(d) 3^m×4^nI had been asked this question in an international level competition.My question is taken from Irrational and Rational Numbers in division Real Numbers of Mathematics – Class 10
Answer» Correct answer is (c) 2^m×5^n To explain: Let’s, take a number where q is of the form 2^m×5^n, say 2^50×5^10and p can be any integer \(\frac {p}{2^{50}\times 5^{10}} = \frac {p \times 5^{40}}{10^{50}}\) The number \(\frac {p \times 5^{40}}{10^{50}}\)will TERMINATE after 50 decimal PLACES. Hence, if q is of the form 2^m×5^n, it will terminate after some decimal places.

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