Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(10,81922\ldots\)
2. \(12,399595\ldots\)
3. \(-18,6\)
4. \(-1,884\)
5. \(18,566\ldots\)
6. \(1,785\)
7. \(16,74\)
8. \(16,34159159\ldots\)
9. \(-20,6\)
10. \(4,3545858\ldots\)
11. \(16,838686\ldots\)
12. \(-19,6\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 10,819\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 108192,22\ldots \\1000x & 10819,22\ldots \\\hline9000x & 97373,00\ldots \end{array}\Leftrightarrow x = \dfrac{97373}{9000}\)
2. \(x = 12,39\textbf{95}\textbf{95}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 123995,9595\ldots \\100x & 1239,9595\ldots \\\hline9900x & 122756,0000\ldots \end{array}\Leftrightarrow x = \dfrac{122756}{9900}= \dfrac{30689}{2475}\)
3. \(-18,6=\dfrac{-186}{10}=\dfrac{-93}{5}\)
4. \(-1,884=\dfrac{-1884}{1000}=\dfrac{-471}{250}\)
5. \(x = 18,5\textbf{6}\textbf{6}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1856,66\ldots \\10x & 185,66\ldots \\\hline90x & 1671,00\ldots \end{array}\Leftrightarrow x = \dfrac{1671}{90}= \dfrac{557}{30}\)
6. \(1,785=\dfrac{1785}{1000}=\dfrac{357}{200}\)
7. \(16,74=\dfrac{1674}{100}=\dfrac{837}{50}\)
8. \(x = 16,34\textbf{159}\textbf{159}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1634159,159159\ldots \\100x & 1634,159159\ldots \\\hline99900x & 1632525,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1632525}{99900}= \dfrac{21767}{1332}\)
9. \(-20,6=\dfrac{-206}{10}=\dfrac{-103}{5}\)
10. \(x = 4,354\textbf{58}\textbf{58}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 435458,5858\ldots \\1000x & 4354,5858\ldots \\\hline99000x & 431104,0000\ldots \end{array}\Leftrightarrow x = \dfrac{431104}{99000}= \dfrac{53888}{12375}\)
11. \(x = 16,83\textbf{86}\textbf{86}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 168386,8686\ldots \\100x & 1683,8686\ldots \\\hline9900x & 166703,0000\ldots \end{array}\Leftrightarrow x = \dfrac{166703}{9900}\)
12. \(-19,6=\dfrac{-196}{10}=\dfrac{-98}{5}\)