Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(-7,80\)
2. \(7,463581581\ldots\)
3. \(13,6733\ldots\)
4. \(4,6\)
5. \(12,2719719\ldots\)
6. \(19,36\)
7. \(-4,463\)
8. \(1,62\)
9. \(4,59789789\ldots\)
10. \(-8,3\)
11. \(5,96754754\ldots\)
12. \(1,33\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(-7,80=\dfrac{-780}{100}=\dfrac{-39}{5}\)
2. \(x = 7,463\textbf{581}\textbf{581}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 7463581{,}581581\ldots \\1000x & 7463{,}581581\ldots \\\hline999000x & 7456118,000000\ldots \end{array}\Leftrightarrow x = \dfrac{7456118}{999000}= \dfrac{3728059}{499500}\)
3. \(x = 13,67\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 13673{,}33\ldots \\100x & 1367{,}33\ldots \\\hline900x & 12306,00\ldots \end{array}\Leftrightarrow x = \dfrac{12306}{900}= \dfrac{2051}{150}\)
4. \(4,6=\dfrac{46}{10}=\dfrac{23}{5}\)
5. \(x = 12,2\textbf{719}\textbf{719}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 122719{,}719719\ldots \\10x & 122{,}719719\ldots \\\hline9990x & 122597,000000\ldots \end{array}\Leftrightarrow x = \dfrac{122597}{9990}\)
6. \(19,36=\dfrac{1936}{100}=\dfrac{484}{25}\)
7. \(-4,463=\dfrac{-4463}{1000}\)
8. \(1,62=\dfrac{162}{100}=\dfrac{81}{50}\)
9. \(x = 4,59\textbf{789}\textbf{789}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 459789{,}789789\ldots \\100x & 459{,}789789\ldots \\\hline99900x & 459330,000000\ldots \end{array}\Leftrightarrow x = \dfrac{459330}{99900}= \dfrac{15311}{3330}\)
10. \(-8,3=\dfrac{-83}{10}\)
11. \(x = 5,96\textbf{754}\textbf{754}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 596754{,}754754\ldots \\100x & 596{,}754754\ldots \\\hline99900x & 596158,000000\ldots \end{array}\Leftrightarrow x = \dfrac{596158}{99900}= \dfrac{298079}{49950}\)
12. \(x = 1,\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 13{,}33\ldots \\1x & 1{,}33\ldots \\\hline9x & 12,00\ldots \end{array}\Leftrightarrow x = \dfrac{12}{9}= \dfrac{4}{3}\)