यदि एक परिमेय संख्या का हर 2n5m के रूप में है, जहाँ n और m ऋणेतर पूर्णांक हैं, तो संख्या का दशमलव प्रसार क्या होगा?

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  1. असांत लेकिन आवर्ती
  2. निर्धारित नहीं किया जा सकता
  3. सांत
  4. असांत और अनावर्ती

Answer (Detailed Solution Below)

Option 3 : सांत
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गणना:

एक परिमेय संख्या सांत होती है यदि इसे p/(2n×5m) के रूप में व्यक्त किया जा सकता है। वह परिमेय संख्या, जिसका हर ऐसी संख्या है जिसका 2 या 5 के अलावा कोई अन्य गुणनखंड नहीं है, दशमलव बिंदु के बाद कभी न कभी सांत हो जाएगी।

∴ संख्या का दशमलव प्रसार सांत है। 

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