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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: 13/3125

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
13/3125

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Factorizing the denominator, we get,
3125 = 5 × 5 × 5 = 5^5
Since, the denominator has only 5 as its factor, 13/3125 has a terminating decimal expansion.

Thanks

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