Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(13,685353\ldots\)
2. \(4,114848\ldots\)
3. \(-7,36\)
4. \(10,77\)
5. \(18,455\)
6. \(6,8874874\ldots\)
7. \(4,7638638\ldots\)
8. \(-15,4\)
9. \(14,7171\ldots\)
10. \(-7,64\)
11. \(8,85\)
12. \(9,66\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 13,68\textbf{53}\textbf{53}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 136853{,}5353\ldots \\100x & 1368{,}5353\ldots \\\hline9900x & 135485,0000\ldots \end{array}\Leftrightarrow x = \dfrac{135485}{9900}= \dfrac{27097}{1980}\)
2. \(x = 4,11\textbf{48}\textbf{48}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 41148{,}4848\ldots \\100x & 411{,}4848\ldots \\\hline9900x & 40737,0000\ldots \end{array}\Leftrightarrow x = \dfrac{40737}{9900}= \dfrac{13579}{3300}\)
3. \(-7,36=\dfrac{-736}{100}=\dfrac{-184}{25}\)
4. \(10,77=\dfrac{1077}{100}\)
5. \(18,455=\dfrac{18455}{1000}=\dfrac{3691}{200}\)
6. \(x = 6,8\textbf{874}\textbf{874}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 68874{,}874874\ldots \\10x & 68{,}874874\ldots \\\hline9990x & 68806,000000\ldots \end{array}\Leftrightarrow x = \dfrac{68806}{9990}= \dfrac{34403}{4995}\)
7. \(x = 4,7\textbf{638}\textbf{638}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 47638{,}638638\ldots \\10x & 47{,}638638\ldots \\\hline9990x & 47591,000000\ldots \end{array}\Leftrightarrow x = \dfrac{47591}{9990}\)
8. \(-15,4=\dfrac{-154}{10}=\dfrac{-77}{5}\)
9. \(x = 14,\textbf{71}\textbf{71}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1471{,}7171\ldots \\1x & 14{,}7171\ldots \\\hline99x & 1457,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1457}{99}\)
10. \(-7,64=\dfrac{-764}{100}=\dfrac{-191}{25}\)
11. \(8,85=\dfrac{885}{100}=\dfrac{177}{20}\)
12. \(x = 9,\textbf{6}\textbf{6}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 96{,}66\ldots \\1x & 9{,}66\ldots \\\hline9x & 87,00\ldots \end{array}\Leftrightarrow x = \dfrac{87}{9}= \dfrac{29}{3}\)