Discussion
The value of \(0.\overline{4} + 0.\overline{6}\) is :
Answer: B
The value is \(1\frac{1}{9}\).
A single repeating digit converts to that digit over 9: \(0.\overline{4} = \frac{4}{9}\) and \(0.\overline{6} = \frac{6}{9}\).
\[ \begin{aligned} 0.\overline{4} + 0.\overline{6} &= \frac{4}{9} + \frac{6}{9} \\ &= \frac{10}{9} = 1\frac{1}{9} \end{aligned} \]
Answering 1 treats the decimals as 0.4 and 0.6 and ignores the bars. \(1\frac{1}{10}\) comes from writing the recurring parts over 10 instead of 9, and \(1\frac{2}{9}\) is an addition slip.
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