Question on: SS3 Mathematics - Surd
Express \(8.\ddot{37}\) as a rational number
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A
\(\frac{829}{99}\)
B
\(\frac{82}{9}\)
C
\(\frac{850}{99}\)
D
\(\frac{393}{99}\)
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Correct Option: A
\[8.\ddot{37} = 8.373737\ldots\]
Let this equal \(x\)
\(x = 8.\ddot{37} = 8.373737\ldots\) [1]
Multiply both sides by 100
\(100x = 837.3737\ldots\) [2]
Subtract [1] from [2]
\[99x = 829\]
\(x = \frac{829}{99}\)
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