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Neha says, “Every non-terminating decimal expansion is irrational.” Which of the following examples proves her statement wrong?नेहा कहती है, “हर अनंत दशमलव प्रसार अपरिमेय होता है।” निम्नलिखित में से कौन-सा उदाहरण उसकी बात को गलत सिद्ध करता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(0.333...\)\(0.333...\)
Since \(0.333...=1/3\), it is non-terminating yet repeating, so it is rational. In contrast, \(\sqrt{2}\) and \(\pi\) are non-repeating. Exam tip: recurring decimals are rational.क्योंकि \(0.333...=1/3\), इसका दशमलव प्रसार अनंत लेकिन आवर्ती है; अतः यह परिमेय है। \(\sqrt{2}\) और \(\pi\) अनावर्ती अपरिमेय हैं। परीक्षा-टिप: आवर्ती दशमलव हमेशा परिमेय होता है।
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