Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(19,478\)
2. \(-4,97\)
3. \(-6,4\)
4. \(4,8277\ldots\)
5. \(2,790923923\ldots\)
6. \(-8,7\)
7. \(10,88\)
8. \(17,2020\ldots\)
9. \(-12,30\)
10. \(9,85757\ldots\)
11. \(3,26682682\ldots\)
12. \(5,17733\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(19,478=\dfrac{19478}{1000}=\dfrac{9739}{500}\)
2. \(-4,97=\dfrac{-497}{100}\)
3. \(-6,4=\dfrac{-64}{10}=\dfrac{-32}{5}\)
4. \(x = 4,82\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 4827{,}77\ldots \\100x & 482{,}77\ldots \\\hline900x & 4345,00\ldots \end{array}\Leftrightarrow x = \dfrac{4345}{900}= \dfrac{869}{180}\)
5. \(x = 2,790\textbf{923}\textbf{923}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 2790923{,}923923\ldots \\1000x & 2790{,}923923\ldots \\\hline999000x & 2788133,000000\ldots \end{array}\Leftrightarrow x = \dfrac{2788133}{999000}\)
6. \(-8,7=\dfrac{-87}{10}\)
7. \(10,88=\dfrac{1088}{100}=\dfrac{272}{25}\)
8. \(x = 17,\textbf{20}\textbf{20}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1720{,}220\ldots \\1x & 17{,}202\ldots \\\hline99x & 1703,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1703}{99}\)
9. \(-12,30=\dfrac{-1230}{100}=\dfrac{-123}{10}\)
10. \(x = 9,8\textbf{57}\textbf{57}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 9857{,}5757\ldots \\10x & 98{,}5757\ldots \\\hline990x & 9759,0000\ldots \end{array}\Leftrightarrow x = \dfrac{9759}{990}= \dfrac{3253}{330}\)
11. \(x = 3,26\textbf{682}\textbf{682}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 326682{,}682682\ldots \\100x & 326{,}682682\ldots \\\hline99900x & 326356,000000\ldots \end{array}\Leftrightarrow x = \dfrac{326356}{99900}= \dfrac{81589}{24975}\)
12. \(x = 5,177\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 51773{,}33\ldots \\1000x & 5177{,}33\ldots \\\hline9000x & 46596,00\ldots \end{array}\Leftrightarrow x = \dfrac{46596}{9000}= \dfrac{3883}{750}\)