Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(2,477\)
2. \(20,44\ldots\)
3. \(3,82\)
4. \(7,606606\ldots\)
5. \(-13,15\)
6. \(3,9\)
7. \(3,544\ldots\)
8. \(-11,8\)
9. \(20,4799\ldots\)
10. \(10,79611\ldots\)
11. \(7,8488\ldots\)
12. \(5,3\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(2,477=\dfrac{2477}{1000}\)
2. \(x = 20,\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 204{,}44\ldots \\1x & 20{,}44\ldots \\\hline9x & 184,00\ldots \end{array}\Leftrightarrow x = \dfrac{184}{9}\)
3. \(3,82=\dfrac{382}{100}=\dfrac{191}{50}\)
4. \(x = 7,\textbf{606}\textbf{606}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 7606{,}606606\ldots \\1x & 7{,}606606\ldots \\\hline999x & 7599,000000\ldots \end{array}\Leftrightarrow x = \dfrac{7599}{999}= \dfrac{2533}{333}\)
5. \(-13,15=\dfrac{-1315}{100}=\dfrac{-263}{20}\)
6. \(3,9=\dfrac{39}{10}\)
7. \(x = 3,5\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 354{,}44\ldots \\10x & 35{,}44\ldots \\\hline90x & 319,00\ldots \end{array}\Leftrightarrow x = \dfrac{319}{90}\)
8. \(-11,8=\dfrac{-118}{10}=\dfrac{-59}{5}\)
9. \(x = 20,47\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 20479{,}99\ldots \\100x & 2047{,}99\ldots \\\hline900x & 18432,00\ldots \end{array}\Leftrightarrow x = \dfrac{18432}{900}= \dfrac{512}{25}\)
10. \(x = 10,796\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 107961{,}11\ldots \\1000x & 10796{,}11\ldots \\\hline9000x & 97165,00\ldots \end{array}\Leftrightarrow x = \dfrac{97165}{9000}= \dfrac{19433}{1800}\)
11. \(x = 7,84\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 7848{,}88\ldots \\100x & 784{,}88\ldots \\\hline900x & 7064,00\ldots \end{array}\Leftrightarrow x = \dfrac{7064}{900}= \dfrac{1766}{225}\)
12. \(5,3=\dfrac{53}{10}\)