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 terminating decimal only when q is of the form _________(a) 3^m×5^n(b) 2^m×6^n(c) 2^m×5^n(d) 7^m×5^nThis question was addressed to me during an interview.Question is from Irrational and Rational Numbers topic 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 terminating decimal only when q is of the form _________(a) 3^m×5^n(b) 2^m×6^n(c) 2^m×5^n(d) 7^m×5^nThis question was addressed to me during an interview.Question is from Irrational and Rational Numbers topic in division Real Numbers of Mathematics – Class 10
Answer» The correct answer is (b) 2^m×6^n To elaborate: 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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