Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(11,27\)
2. \(4,283326326\ldots\)
3. \(19,23636\ldots\)
4. \(12,4130130\ldots\)
5. \(3,9619619\ldots\)
6. \(17,2525\ldots\)
7. \(2,6\)
8. \(10,301717\ldots\)
9. \(15,9090\ldots\)
10. \(-20,93\)
11. \(-5,38\)
12. \(15,928928928\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(11,27=\dfrac{1127}{100}\)
2. \(x = 4,283\textbf{326}\textbf{326}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 4283326{,}326326\ldots \\1000x & 4283{,}326326\ldots \\\hline999000x & 4279043,000000\ldots \end{array}\Leftrightarrow x = \dfrac{4279043}{999000}\)
3. \(x = 19,2\textbf{36}\textbf{36}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 19236{,}3636\ldots \\10x & 192{,}3636\ldots \\\hline990x & 19044,0000\ldots \end{array}\Leftrightarrow x = \dfrac{19044}{990}= \dfrac{1058}{55}\)
4. \(x = 12,4\textbf{130}\textbf{130}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 124130{,}13130\ldots \\10x & 124{,}13013\ldots \\\hline9990x & 124006,000000\ldots \end{array}\Leftrightarrow x = \dfrac{124006}{9990}= \dfrac{62003}{4995}\)
5. \(x = 3,9\textbf{619}\textbf{619}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 39619{,}619619\ldots \\10x & 39{,}619619\ldots \\\hline9990x & 39580,000000\ldots \end{array}\Leftrightarrow x = \dfrac{39580}{9990}= \dfrac{3958}{999}\)
6. \(x = 17,\textbf{25}\textbf{25}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1725{,}2525\ldots \\1x & 17{,}2525\ldots \\\hline99x & 1708,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1708}{99}\)
7. \(2,6=\dfrac{26}{10}=\dfrac{13}{5}\)
8. \(x = 10,30\textbf{17}\textbf{17}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 103017{,}1717\ldots \\100x & 1030{,}1717\ldots \\\hline9900x & 101987,0000\ldots \end{array}\Leftrightarrow x = \dfrac{101987}{9900}\)
9. \(x = 15,\textbf{90}\textbf{90}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1590{,}990\ldots \\1x & 15{,}909\ldots \\\hline99x & 1575,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1575}{99}= \dfrac{175}{11}\)
10. \(-20,93=\dfrac{-2093}{100}\)
11. \(-5,38=\dfrac{-538}{100}=\dfrac{-269}{50}\)
12. \(x = 15,928\textbf{928}\textbf{928}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 15928928{,}928928\ldots \\1000x & 15928{,}928928\ldots \\\hline999000x & 15913000,000000\ldots \end{array}\Leftrightarrow x = \dfrac{15913000}{999000}= \dfrac{15913}{999}\)