Question
Download Solution PDF0.135135.... को p/q के रूप में लिखिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
0.135135....
प्रयुक्त अवधारणा:
(p/q) प्रकार की संख्याएँ, जहाँ q ≠ 0 और p और q पूर्णांक हैं, परिमेय संख्या कहलाती हैं।
गणना
माना x = 0.135135.... ---- (1)
समीकरण 1 में दोनों पक्ष में 1000 से गुणा कीजिये, हमारे पास है
1000x = 135.135... ---- (2)
समीकरण (1) को समीकरण (2) से घटाने पर, हमें प्राप्त होता है
1000x - x = 135.135... - 0.135135....
⇒ 999x = 135
⇒ x = 135/999
⇒ x = 45/333
⇒ x = 5/37
∴ 0.135135.... को p/q के रूप में 5/37 लिखा जा सकता है।
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