Decimals

a fully simplified fraction

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$0.\overline{42}\cdot 100=42.\overline{42}$

    $\underline{0.\overline{42}\cdot 1=\ 0.\overline{42}}$

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

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