Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(18,365959\ldots\)
2. \(-20,58\)
3. \(-4,41\)
4. \(8,797742742\ldots\)
5. \(3,97768768\ldots\)
6. \(12,6\)
7. \(12,4864864\ldots\)
8. \(9,93434\ldots\)
9. \(-2,8\)
10. \(-5,787\)
11. \(-16,7\)
12. \(19,9816816\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 18,36\textbf{59}\textbf{59}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 183659,5959\ldots \\100x & 1836,5959\ldots \\\hline9900x & 181823,0000\ldots \end{array}\Leftrightarrow x = \dfrac{181823}{9900}\)
2. \(-20,58=\dfrac{-2058}{100}=\dfrac{-1029}{50}\)
3. \(-4,41=\dfrac{-441}{100}\)
4. \(x = 8,797\textbf{742}\textbf{742}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 8797742,742742\ldots \\1000x & 8797,742742\ldots \\\hline999000x & 8788945,000000\ldots \end{array}\Leftrightarrow x = \dfrac{8788945}{999000}= \dfrac{1757789}{199800}\)
5. \(x = 3,97\textbf{768}\textbf{768}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 397768,768768\ldots \\100x & 397,768768\ldots \\\hline99900x & 397371,000000\ldots \end{array}\Leftrightarrow x = \dfrac{397371}{99900}= \dfrac{132457}{33300}\)
6. \(12,6=\dfrac{126}{10}=\dfrac{63}{5}\)
7. \(x = 12,4\textbf{864}\textbf{864}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 124864,864864\ldots \\10x & 124,864864\ldots \\\hline9990x & 124740,000000\ldots \end{array}\Leftrightarrow x = \dfrac{124740}{9990}= \dfrac{462}{37}\)
8. \(x = 9,9\textbf{34}\textbf{34}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 9934,3434\ldots \\10x & 99,3434\ldots \\\hline990x & 9835,0000\ldots \end{array}\Leftrightarrow x = \dfrac{9835}{990}= \dfrac{1967}{198}\)
9. \(-2,8=\dfrac{-28}{10}=\dfrac{-14}{5}\)
10. \(-5,787=\dfrac{-5787}{1000}\)
11. \(-16,7=\dfrac{-167}{10}\)
12. \(x = 19,9\textbf{816}\textbf{816}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 199816,816816\ldots \\10x & 199,816816\ldots \\\hline9990x & 199617,000000\ldots \end{array}\Leftrightarrow x = \dfrac{199617}{9990}= \dfrac{66539}{3330}\)