Question
Download Solution PDF\(0.1\overline7\) को \(\frac{p}{q}\) के रूप में व्यक्त करें, जहाँ p और q पूर्णांक हैं और q ≠ 0 है।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
\(0.1\overline7\) को \(\frac{p}{q}\) के रूप में व्यक्त करें, जहाँ p और q पूर्णांक हैं और q ≠ 0 है।
प्रयुक्त अवधारणा:
वे सभी संख्याएँ जिन्हें p/q के रूप में बदला जा सकता है, जहाँ p, q पूर्णांक हैं और q ≠ 0, परिमेय संख्याएँ कहलाती हैं।
गणना:
मान लीजिए,
x = 0.1777… -(1)
तो, 10x = 1.777… —(2)
(2) को (1) से घटाने पर, हम पाते हैं,
⇒ 10x - x = 1.777 - 0.1777
⇒ 9x = 1.6 x = \(1.6\over 9\)
⇒ x = \(16\over 90\)
⇒ \(x = {p\over q} = {8\over45}\)
इसलिए, 'विकल्प 4' सही है।
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