Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(12,88195195\ldots\)
2. \(2,9\)
3. \(-2,95\)
4. \(-15,65\)
5. \(-10,3\)
6. \(14,7\)
7. \(18,6011\ldots\)
8. \(7,5\)
9. \(11,984984\ldots\)
10. \(4,8845845\ldots\)
11. \(18,49635635\ldots\)
12. \(17,737\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 12,88\textbf{195}\textbf{195}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1288195{,}195195\ldots \\100x & 1288{,}195195\ldots \\\hline99900x & 1286907,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1286907}{99900}= \dfrac{428969}{33300}\)
2. \(2,9=\dfrac{29}{10}\)
3. \(-2,95=\dfrac{-295}{100}=\dfrac{-59}{20}\)
4. \(-15,65=\dfrac{-1565}{100}=\dfrac{-313}{20}\)
5. \(-10,3=\dfrac{-103}{10}\)
6. \(14,7=\dfrac{147}{10}\)
7. \(x = 18,60\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 18601{,}11\ldots \\100x & 1860{,}11\ldots \\\hline900x & 16741,00\ldots \end{array}\Leftrightarrow x = \dfrac{16741}{900}\)
8. \(7,5=\dfrac{75}{10}=\dfrac{15}{2}\)
9. \(x = 11,\textbf{984}\textbf{984}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 11984{,}984984\ldots \\1x & 11{,}984984\ldots \\\hline999x & 11973,000000\ldots \end{array}\Leftrightarrow x = \dfrac{11973}{999}= \dfrac{3991}{333}\)
10. \(x = 4,8\textbf{845}\textbf{845}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 48845{,}845845\ldots \\10x & 48{,}845845\ldots \\\hline9990x & 48797,000000\ldots \end{array}\Leftrightarrow x = \dfrac{48797}{9990}\)
11. \(x = 18,49\textbf{635}\textbf{635}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1849635{,}635635\ldots \\100x & 1849{,}635635\ldots \\\hline99900x & 1847786,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1847786}{99900}= \dfrac{923893}{49950}\)
12. \(17,737=\dfrac{17737}{1000}\)