Question
Download Solution PDF\(0.1\overline7\) ని \(\frac{p}{q}\) రూపంలో వ్యక్తపరచండి, ఇక్కడ p మరియు q పూర్ణ సంఖ్యలు మరియు q ≠ 0.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇచ్చినది:
\(0.1\overline7\) ని \(\frac{p}{q}\) రూపంలో వ్యక్తపరచండి, ఇక్కడ p మరియు q పూర్ణ సంఖ్యలు మరియు q ≠ 0.
ఉపయోగించిన భావన:
p, q పూర్ణ సంఖ్యలు మరియు q ≠ 0ని p/q రూపంలోకి మార్చగల అన్ని సంఖ్యలను ఆకరణీయ సంఖ్యలు అంటారు.
గణన:
అనుకుందాం,
x = 0.1777… —(1)
కాబట్టి, 10x = 1.777… —(2)
(1) నుండి (2) తీసివేయగా, మనకు ఇలా లభిస్తుంది,
⇒ 10x - x = 1.777 - 0.1777
⇒ 9x = 1.6 x = \(1.6\over 9\)
⇒ x = \(16\over 90\)
⇒ \(x = {p\over q} = {8\over45}\)
కాబట్టి, 'ఎంపిక 4' సరైనది.
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