Express \(0.4\overline{32}\) in the form of \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q \neq 0\).
\(\frac{214}{495}\)
Let \(x = 0.4\overline{32} = 0.4323232\ldots\). Multiplying suitably to align the repeating block: \(1000x = 432.3232\ldots\) and \(10x = 4.3232\ldots\). Subtracting: \(990x = 432.32\ldots - 4.32\ldots = 428\).
So \(x = \dfrac{428}{990} = \dfrac{214}{495}\) (dividing numerator and denominator by 2).
Hence, \(\dfrac{214}{495}\) is correct.
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