Question
Download Solution PDFsimplify the given expression.
\(11.45\overline{65} \div 2.\overline {67}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(11.45\overline{65} \div 2.\overline {67}\)
Calculation:
n order to simplify, we need to convert them in the form of \(p\over q\)
For \(11.45\overline{65}\).....
Let x = 11.4565656565....
Multiplying both sides with 100
100x = 1145.656565......
100x = 1134.20 + 11.456565....
100x = 1134.20 + x
99x = \(113420\over100\)
x = \(113420\over9900\)
For \(2.\overline{67}\).....
Let x = 2.676767....
Multiplying both sides with 100
100x = 267.6767.......
100x = 265 + 2.676767....
100x = 265 + x
99x = 265
x = \(265\over99\)
Now, we have
\(11.45\overline{65} \div 2.\overline {67}\) = \({113420\over9900}\div{265\over99}\)
= \({113420\over9900}\times{99\over265}\)
= \({428\over100}={107\over25}\)
= \({4}{7\over25}\)
Hence, the correct answer is \({4}{7\over25}\).
Last updated on Jun 30, 2025
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