Verified by Ajay Kumar
What is the simplest form of the fraction represented by the recurring decimal 0.454545...?
\(\frac{45}{91}\)
\(\frac{5}{11}\)
\(\frac{9}{20}\)
\(\frac{1}{11}\)
Answer: B
Let \(x=0.454545\ldots\). Since two digits repeat, \(100x=45.454545\ldots\). Subtracting, \(100x-x=45\), so \(99x=45\). Therefore, \(x=\frac{45}{99}=\frac{5}{11}\). Trick: Write the repeating two-digit block over 99 and simplify.
आवर्ती दशमलव 0.454545... द्वारा दर्शाई गई भिन्न का सरलतम रूप क्या है?
\(\frac{45}{91}\)
\(\frac{5}{11}\)
\(\frac{9}{20}\)
\(\frac{1}{11}\)
उत्तर: B
मान लीजिए \(x=0.454545\ldots\)। दो अंक दोहराए जा रहे हैं, इसलिए \(100x=45.454545\ldots\)। घटाने पर \(100x-x=45\), अर्थात \(99x=45\)। अतः \(x=\frac{45}{99}=\frac{5}{11}\)। ट्रिक: दो अंकों के आवर्ती दशमलव में दोहराए जाने वाले अंकों को 99 के ऊपर लिखकर सरल करें।
Community answers
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- Option B\(\frac{5}{11}\)
45 ka Bar maan kr bhi direct kr skte the 45/99 = 5/11
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