Question
Download Solution PDF\(0.13\overline {241} \)-কে \(\frac{p}{q}\) আকারে প্রকাশ করুন, যেখানে p এবং q পূর্ণসংখ্যা এবং q \( \ne \) 0.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
মান = \(0.13\overline {241} \) = 0.13241241241......
গণনা:
ধরি, x = \(0.13\overline {241} \)........... (1)
সমীকরণ (1) কে 100 দ্বারা গুণ করুন, আমরা পাই (কারণ দুটি অঙ্ক আছে যেগুলিতে কোনো বার নেই)
100x = 13.241241...... (2)
সমীকরণ (2) কে 1000 দ্বারা গুণ করুন, আমরা পাই (কারণ তিনটি অঙ্ক আছে যেগুলিতে বার আছে)
100000x = 13241.241241....... (3)
এখন, সমীকরণ (3) থেকে সমীকরণ (2) বিয়োগ করুন, আমরা পাই
99900x = 13228
x = \(\frac{13228}{99900}\)
x এর মান সরল করে, আমরা পাই x = \(\frac{{3307}}{{24975}}\)
সুতরাং, সঠিক উত্তর হলো \(\frac{{3307}}{{24975}}\).
Last updated on Jul 11, 2025
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