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Write $\frac{99}{100} (0.\overline{42})$ as a fully simplified fraction.

 Oct 18, 2022
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a fully simplified fraction

 

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\(0.\overline{42}\cdot 100=42.\overline{42}\)

    \(\underline{0.\overline{42}\cdot 1=\ 0.\overline{42}}\)

  \(0.\overline{42}\cdot 99=42\\ 0.\overline{42}=\dfrac{42}{99}\\ \color{blue}\dfrac{99}{100}\cdot 0.\overline{42}=\dfrac{99\cdot 42}{100\cdot 99}=\dfrac{21}{50}\)

laugh  !

 Oct 18, 2022
edited by asinus  Oct 18, 2022

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