Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(19,2121\ldots\)
2. \(1,49898\ldots\)
3. \(-5,7\)
4. \(12,3599\ldots\)
5. \(7,6\)
6. \(15,42\)
7. \(-19,383\)
8. \(12,4\)
9. \(12,7561561\ldots\)
10. \(-16,8\)
11. \(-1,2\)
12. \(-2,838\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 19,\textbf{21}\textbf{21}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1921{,}2121\ldots \\1x & 19{,}2121\ldots \\\hline99x & 1902,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1902}{99}= \dfrac{634}{33}\)
2. \(x = 1,4\textbf{98}\textbf{98}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 1498{,}9898\ldots \\10x & 14{,}9898\ldots \\\hline990x & 1484,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1484}{990}= \dfrac{742}{495}\)
3. \(-5,7=\dfrac{-57}{10}\)
4. \(x = 12,35\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 12359{,}99\ldots \\100x & 1235{,}99\ldots \\\hline900x & 11124,00\ldots \end{array}\Leftrightarrow x = \dfrac{11124}{900}= \dfrac{309}{25}\)
5. \(7,6=\dfrac{76}{10}=\dfrac{38}{5}\)
6. \(15,42=\dfrac{1542}{100}=\dfrac{771}{50}\)
7. \(-19,383=\dfrac{-19383}{1000}\)
8. \(12,4=\dfrac{124}{10}=\dfrac{62}{5}\)
9. \(x = 12,7\textbf{561}\textbf{561}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 127561{,}561561\ldots \\10x & 127{,}561561\ldots \\\hline9990x & 127434,000000\ldots \end{array}\Leftrightarrow x = \dfrac{127434}{9990}= \dfrac{21239}{1665}\)
10. \(-16,8=\dfrac{-168}{10}=\dfrac{-84}{5}\)
11. \(-1,2=\dfrac{-12}{10}=\dfrac{-6}{5}\)
12. \(-2,838=\dfrac{-2838}{1000}=\dfrac{-1419}{500}\)