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Rima says that the decimal expansion of \(\frac{13}{30}\) will terminate because 30 has both 2 and 5 as factors. What is the error in Rima’s statement?रीमा कहती है कि \(\frac{13}{30}\) का दशमलव प्रसार सांत होगा, क्योंकि 30 में 2 और 5 दोनों गुणनखंड हैं। रीमा के कथन में त्रुटि क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Since 30 has 3 as a factor along with 2 and 5, the decimal expansion will be non-terminating recurring.30 में 2 और 5 के साथ 3 भी गुणनखंड है, इसलिए दशमलव प्रसार असांत आवर्ती होगा।
Since 13 and 30 are coprime, 30 is the denominator in lowest form. As \(30=2\times3\times5\) contains 3, the decimal is non-terminating recurring. Exam tip: check prime factors of the reduced denominator.13 और 30 सह-अभाज्य हैं, इसलिए 30 ही न्यूनतम रूप का हर है। \(30=2\times3\times5\) में 3 भी है, अतः दशमलव असांत आवर्ती होगा। परीक्षा में हर के अभाज्य गुणनखंड जाँचें।
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