Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(5,6\)
2. \(8,632632\ldots\)
3. \(2,88\ldots\)
4. \(8,711\ldots\)
5. \(3,277\ldots\)
6. \(12,746746\ldots\)
7. \(14,54744\ldots\)
8. \(14,5\)
9. \(-6,951\)
10. \(20,6142142\ldots\)
11. \(-11,325\)
12. \(20,7603737\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(5,6=\dfrac{56}{10}=\dfrac{28}{5}\)
2. \(x = 8,\textbf{632}\textbf{632}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 8632,632632\ldots \\1x & 8,632632\ldots \\\hline999x & 8624,000000\ldots \end{array}\Leftrightarrow x = \dfrac{8624}{999}\)
3. \(x = 2,\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 28,88\ldots \\1x & 2,88\ldots \\\hline9x & 26,00\ldots \end{array}\Leftrightarrow x = \dfrac{26}{9}\)
4. \(x = 8,7\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 871,11\ldots \\10x & 87,11\ldots \\\hline90x & 784,00\ldots \end{array}\Leftrightarrow x = \dfrac{784}{90}= \dfrac{392}{45}\)
5. \(x = 3,2\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 327,77\ldots \\10x & 32,77\ldots \\\hline90x & 295,00\ldots \end{array}\Leftrightarrow x = \dfrac{295}{90}= \dfrac{59}{18}\)
6. \(x = 12,\textbf{746}\textbf{746}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 12746,746746\ldots \\1x & 12,746746\ldots \\\hline999x & 12734,000000\ldots \end{array}\Leftrightarrow x = \dfrac{12734}{999}\)
7. \(x = 14,547\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 145474,44\ldots \\1000x & 14547,44\ldots \\\hline9000x & 130927,00\ldots \end{array}\Leftrightarrow x = \dfrac{130927}{9000}\)
8. \(14,5=\dfrac{145}{10}=\dfrac{29}{2}\)
9. \(-6,951=\dfrac{-6951}{1000}\)
10. \(x = 20,6\textbf{142}\textbf{142}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 206142,142142\ldots \\10x & 206,142142\ldots \\\hline9990x & 205936,000000\ldots \end{array}\Leftrightarrow x = \dfrac{205936}{9990}= \dfrac{102968}{4995}\)
11. \(-11,325=\dfrac{-11325}{1000}=\dfrac{-453}{40}\)
12. \(x = 20,760\textbf{37}\textbf{37}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 2076037,3737\ldots \\1000x & 20760,3737\ldots \\\hline99000x & 2055277,0000\ldots \end{array}\Leftrightarrow x = \dfrac{2055277}{99000}\)