Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(4,6\)
2. \(17,88\)
3. \(15,369369\ldots\)
4. \(9,69762762\ldots\)
5. \(8,9753535\ldots\)
6. \(3,34\)
7. \(19,224\)
8. \(-4,542\)
9. \(14,1775151\ldots\)
10. \(4,685685\ldots\)
11. \(8,27792792\ldots\)
12. \(11,381313\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(4,6=\dfrac{46}{10}=\dfrac{23}{5}\)
2. \(17,88=\dfrac{1788}{100}=\dfrac{447}{25}\)
3. \(x = 15,\textbf{369}\textbf{369}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 15369{,}369369\ldots \\1x & 15{,}369369\ldots \\\hline999x & 15354,000000\ldots \end{array}\Leftrightarrow x = \dfrac{15354}{999}= \dfrac{1706}{111}\)
4. \(x = 9,69\textbf{762}\textbf{762}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 969762{,}762762\ldots \\100x & 969{,}762762\ldots \\\hline99900x & 968793,000000\ldots \end{array}\Leftrightarrow x = \dfrac{968793}{99900}= \dfrac{322931}{33300}\)
5. \(x = 8,975\textbf{35}\textbf{35}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 897535{,}3535\ldots \\1000x & 8975{,}3535\ldots \\\hline99000x & 888560,0000\ldots \end{array}\Leftrightarrow x = \dfrac{888560}{99000}= \dfrac{22214}{2475}\)
6. \(3,34=\dfrac{334}{100}=\dfrac{167}{50}\)
7. \(19,224=\dfrac{19224}{1000}=\dfrac{2403}{125}\)
8. \(-4,542=\dfrac{-4542}{1000}=\dfrac{-2271}{500}\)
9. \(x = 14,177\textbf{51}\textbf{51}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1417751{,}5151\ldots \\1000x & 14177{,}5151\ldots \\\hline99000x & 1403574,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1403574}{99000}= \dfrac{233929}{16500}\)
10. \(x = 4,\textbf{685}\textbf{685}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 4685{,}685685\ldots \\1x & 4{,}685685\ldots \\\hline999x & 4681,000000\ldots \end{array}\Leftrightarrow x = \dfrac{4681}{999}\)
11. \(x = 8,27\textbf{792}\textbf{792}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 827792{,}792792\ldots \\100x & 827{,}792792\ldots \\\hline99900x & 826965,000000\ldots \end{array}\Leftrightarrow x = \dfrac{826965}{99900}= \dfrac{18377}{2220}\)
12. \(x = 11,38\textbf{13}\textbf{13}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 113813{,}1313\ldots \\100x & 1138{,}1313\ldots \\\hline9900x & 112675,0000\ldots \end{array}\Leftrightarrow x = \dfrac{112675}{9900}= \dfrac{4507}{396}\)