Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(18,5858\ldots\)
2. \(9,76262\ldots\)
3. \(0,8989\ldots\)
4. \(-9,90\)
5. \(20,11262262\ldots\)
6. \(4,37171\ldots\)
7. \(5,5502502\ldots\)
8. \(11,6\)
9. \(9,6161\ldots\)
10. \(20,7\)
11. \(4,68322\ldots\)
12. \(-14,86\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 18,\textbf{58}\textbf{58}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1858,5858\ldots \\1x & 18,5858\ldots \\\hline99x & 1840,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1840}{99}\)
2. \(x = 9,7\textbf{62}\textbf{62}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 9762,6262\ldots \\10x & 97,6262\ldots \\\hline990x & 9665,0000\ldots \end{array}\Leftrightarrow x = \dfrac{9665}{990}= \dfrac{1933}{198}\)
3. \(x = 0,\textbf{89}\textbf{89}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 89,8989\ldots \\1x & 0,8989\ldots \\\hline99x & 89,0000\ldots \end{array}\Leftrightarrow x = \dfrac{89}{99}\)
4. \(-9,90=\dfrac{-990}{100}=\dfrac{-99}{10}\)
5. \(x = 20,11\textbf{262}\textbf{262}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 2011262,262262\ldots \\100x & 2011,262262\ldots \\\hline99900x & 2009251,000000\ldots \end{array}\Leftrightarrow x = \dfrac{2009251}{99900}\)
6. \(x = 4,3\textbf{71}\textbf{71}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 4371,7171\ldots \\10x & 43,7171\ldots \\\hline990x & 4328,0000\ldots \end{array}\Leftrightarrow x = \dfrac{4328}{990}= \dfrac{2164}{495}\)
7. \(x = 5,5\textbf{502}\textbf{502}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 55502,502502\ldots \\10x & 55,502502\ldots \\\hline9990x & 55447,000000\ldots \end{array}\Leftrightarrow x = \dfrac{55447}{9990}\)
8. \(11,6=\dfrac{116}{10}=\dfrac{58}{5}\)
9. \(x = 9,\textbf{61}\textbf{61}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 961,6161\ldots \\1x & 9,6161\ldots \\\hline99x & 952,0000\ldots \end{array}\Leftrightarrow x = \dfrac{952}{99}\)
10. \(20,7=\dfrac{207}{10}\)
11. \(x = 4,683\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 46832,22\ldots \\1000x & 4683,22\ldots \\\hline9000x & 42149,00\ldots \end{array}\Leftrightarrow x = \dfrac{42149}{9000}\)
12. \(-14,86=\dfrac{-1486}{100}=\dfrac{-743}{50}\)