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Which of the following rational numbers will have a non-terminating recurring decimal expansion?निम्नलिखित में से किस परिमेय संख्या का दशमलव प्रसार अनंत आवर्ती होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\frac{17}{120}\)\(\frac{17}{120}\)
A rational number has a terminating decimal only when, in lowest form, its denominator has prime factors 2 and/or 5 only. Since \(120=2^3\times3\times5\) includes 3, \(\frac{17}{120}\) is non-terminating recurring. Exam tip: always check the denominator after simplification.सरलतम रूप में किसी परिमेय संख्या का दशमलव प्रसार तभी सांत होता है, जब हर के अभाज्य गुणनखंड केवल 2 और 5 हों। \(120=2^3\times3\times5\) में 3 भी है, इसलिए \(\frac{17}{120}\) अनंत आवर्ती है। परीक्षा टिप: पहले भिन्न को सरलतम रूप में जाँचें।
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