Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(-19,2\)
2. \(14,171818\ldots\)
3. \(8,34\)
4. \(-18,5\)
5. \(2,95\)
6. \(1,3126126\ldots\)
7. \(0,8488\ldots\)
8. \(-5,242\)
9. \(6,215\)
10. \(11,4732732\ldots\)
11. \(10,668460460\ldots\)
12. \(11,757373\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(-19,2=\dfrac{-192}{10}=\dfrac{-96}{5}\)
2. \(x = 14,17\textbf{18}\textbf{18}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 141718{,}1818\ldots \\100x & 1417{,}1818\ldots \\\hline9900x & 140301,0000\ldots \end{array}\Leftrightarrow x = \dfrac{140301}{9900}= \dfrac{15589}{1100}\)
3. \(8,34=\dfrac{834}{100}=\dfrac{417}{50}\)
4. \(-18,5=\dfrac{-185}{10}=\dfrac{-37}{2}\)
5. \(2,95=\dfrac{295}{100}=\dfrac{59}{20}\)
6. \(x = 1,3\textbf{126}\textbf{126}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 13126{,}126126\ldots \\10x & 13{,}126126\ldots \\\hline9990x & 13113,000000\ldots \end{array}\Leftrightarrow x = \dfrac{13113}{9990}= \dfrac{1457}{1110}\)
7. \(x = 0,84\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 848{,}88\ldots \\100x & 84{,}88\ldots \\\hline900x & 764,00\ldots \end{array}\Leftrightarrow x = \dfrac{764}{900}= \dfrac{191}{225}\)
8. \(-5,242=\dfrac{-5242}{1000}=\dfrac{-2621}{500}\)
9. \(6,215=\dfrac{6215}{1000}=\dfrac{1243}{200}\)
10. \(x = 11,4\textbf{732}\textbf{732}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 114732{,}732732\ldots \\10x & 114{,}732732\ldots \\\hline9990x & 114618,000000\ldots \end{array}\Leftrightarrow x = \dfrac{114618}{9990}= \dfrac{19103}{1665}\)
11. \(x = 10,668\textbf{460}\textbf{460}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 10668460{,}46460\ldots \\1000x & 10668{,}46046\ldots \\\hline999000x & 10657792,000000\ldots \end{array}\Leftrightarrow x = \dfrac{10657792}{999000}= \dfrac{1332224}{124875}\)
12. \(x = 11,75\textbf{73}\textbf{73}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 117573{,}7373\ldots \\100x & 1175{,}7373\ldots \\\hline9900x & 116398,0000\ldots \end{array}\Leftrightarrow x = \dfrac{116398}{9900}= \dfrac{58199}{4950}\)