Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(1,529\)
2. \(18,800\)
3. \(13,2020\ldots\)
4. \(6,9378378\ldots\)
5. \(17,55677\ldots\)
6. \(8,8181\ldots\)
7. \(14,716565\ldots\)
8. \(15,2764764\ldots\)
9. \(-7,22\)
10. \(-17,74\)
11. \(-8,75\)
12. \(12,39701701\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(1,529=\dfrac{1529}{1000}\)
2. \(18,800=\dfrac{18800}{1000}=\dfrac{94}{5}\)
3. \(x = 13,\textbf{20}\textbf{20}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1320,220\ldots \\1x & 13,202\ldots \\\hline99x & 1307,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1307}{99}\)
4. \(x = 6,9\textbf{378}\textbf{378}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 69378,378378\ldots \\10x & 69,378378\ldots \\\hline9990x & 69309,000000\ldots \end{array}\Leftrightarrow x = \dfrac{69309}{9990}= \dfrac{2567}{370}\)
5. \(x = 17,556\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 175567,77\ldots \\1000x & 17556,77\ldots \\\hline9000x & 158011,00\ldots \end{array}\Leftrightarrow x = \dfrac{158011}{9000}\)
6. \(x = 8,\textbf{81}\textbf{81}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 881,8181\ldots \\1x & 8,8181\ldots \\\hline99x & 873,0000\ldots \end{array}\Leftrightarrow x = \dfrac{873}{99}= \dfrac{97}{11}\)
7. \(x = 14,71\textbf{65}\textbf{65}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 147165,6565\ldots \\100x & 1471,6565\ldots \\\hline9900x & 145694,0000\ldots \end{array}\Leftrightarrow x = \dfrac{145694}{9900}= \dfrac{72847}{4950}\)
8. \(x = 15,2\textbf{764}\textbf{764}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 152764,764764\ldots \\10x & 152,764764\ldots \\\hline9990x & 152612,000000\ldots \end{array}\Leftrightarrow x = \dfrac{152612}{9990}= \dfrac{76306}{4995}\)
9. \(-7,22=\dfrac{-722}{100}=\dfrac{-361}{50}\)
10. \(-17,74=\dfrac{-1774}{100}=\dfrac{-887}{50}\)
11. \(-8,75=\dfrac{-875}{100}=\dfrac{-35}{4}\)
12. \(x = 12,39\textbf{701}\textbf{701}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1239701,701701\ldots \\100x & 1239,701701\ldots \\\hline99900x & 1238462,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1238462}{99900}= \dfrac{619231}{49950}\)