Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(15,5\)
2. \(-4,8\)
3. \(20,27288\ldots\)
4. \(-12,89\)
5. \(5,7438438\ldots\)
6. \(13,3\)
7. \(-20,67\)
8. \(10,3\)
9. \(7,678\)
10. \(-4,204\)
11. \(5,8080\ldots\)
12. \(3,68471471\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(15,5=\dfrac{155}{10}=\dfrac{31}{2}\)
2. \(-4,8=\dfrac{-48}{10}=\dfrac{-24}{5}\)
3. \(x = 20,272\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 202728,88\ldots \\1000x & 20272,88\ldots \\\hline9000x & 182456,00\ldots \end{array}\Leftrightarrow x = \dfrac{182456}{9000}= \dfrac{22807}{1125}\)
4. \(-12,89=\dfrac{-1289}{100}\)
5. \(x = 5,7\textbf{438}\textbf{438}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 57438,438438\ldots \\10x & 57,438438\ldots \\\hline9990x & 57381,000000\ldots \end{array}\Leftrightarrow x = \dfrac{57381}{9990}= \dfrac{19127}{3330}\)
6. \(13,3=\dfrac{133}{10}\)
7. \(-20,67=\dfrac{-2067}{100}\)
8. \(10,3=\dfrac{103}{10}\)
9. \(7,678=\dfrac{7678}{1000}=\dfrac{3839}{500}\)
10. \(-4,204=\dfrac{-4204}{1000}=\dfrac{-1051}{250}\)
11. \(x = 5,\textbf{80}\textbf{80}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 580,880\ldots \\1x & 5,808\ldots \\\hline99x & 575,0000\ldots \end{array}\Leftrightarrow x = \dfrac{575}{99}\)
12. \(x = 3,68\textbf{471}\textbf{471}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 368471,471471\ldots \\100x & 368,471471\ldots \\\hline99900x & 368103,000000\ldots \end{array}\Leftrightarrow x = \dfrac{368103}{99900}= \dfrac{122701}{33300}\)