Which of the following has a terminating decimal expansion?(a) \(\fra – InterviewSolution

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1.

Which of the following has a terminating decimal expansion?(a) \(\frac{32}{91}\) (b) \(\frac{19}{80}\)(c) \(\frac{23}{45}\)(d) \(\frac{25}{42}\)

Answer»

(b) \(\frac{19}{80}\)

\(\frac{19}{80}\) = \(\frac{19}{2^4\times5}\)

We know 2 and 5 are not factors of 19, so it is in its simplest form.

And (2⁴ × 5) = (2^m × 5ⁿ)

Hence, \(\frac{19}{80}\) is a terminating decimal.

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