Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(7,357070\ldots\)
2. \(9,2121\ldots\)
3. \(9,5901901\ldots\)
4. \(1,76851851\ldots\)
5. \(-15,99\)
6. \(17,3411919\ldots\)
7. \(2,4884242\ldots\)
8. \(9,2355\ldots\)
9. \(18,7185050\ldots\)
10. \(12,5328787\ldots\)
11. \(1,7070\ldots\)
12. \(17,97288\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 7,35\textbf{70}\textbf{70}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 73570{,}770\ldots \\100x & 735{,}707\ldots \\\hline9900x & 72835,0000\ldots \end{array}\Leftrightarrow x = \dfrac{72835}{9900}= \dfrac{14567}{1980}\)
2. \(x = 9,\textbf{21}\textbf{21}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 921{,}2121\ldots \\1x & 9{,}2121\ldots \\\hline99x & 912,0000\ldots \end{array}\Leftrightarrow x = \dfrac{912}{99}= \dfrac{304}{33}\)
3. \(x = 9,5\textbf{901}\textbf{901}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 95901{,}901901\ldots \\10x & 95{,}901901\ldots \\\hline9990x & 95806,000000\ldots \end{array}\Leftrightarrow x = \dfrac{95806}{9990}= \dfrac{47903}{4995}\)
4. \(x = 1,76\textbf{851}\textbf{851}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 176851{,}851851\ldots \\100x & 176{,}851851\ldots \\\hline99900x & 176675,000000\ldots \end{array}\Leftrightarrow x = \dfrac{176675}{99900}= \dfrac{191}{108}\)
5. \(-15,99=\dfrac{-1599}{100}\)
6. \(x = 17,341\textbf{19}\textbf{19}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1734119{,}1919\ldots \\1000x & 17341{,}1919\ldots \\\hline99000x & 1716778,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1716778}{99000}= \dfrac{858389}{49500}\)
7. \(x = 2,488\textbf{42}\textbf{42}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 248842{,}4242\ldots \\1000x & 2488{,}4242\ldots \\\hline99000x & 246354,0000\ldots \end{array}\Leftrightarrow x = \dfrac{246354}{99000}= \dfrac{41059}{16500}\)
8. \(x = 9,23\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 9235{,}55\ldots \\100x & 923{,}55\ldots \\\hline900x & 8312,00\ldots \end{array}\Leftrightarrow x = \dfrac{8312}{900}= \dfrac{2078}{225}\)
9. \(x = 18,718\textbf{50}\textbf{50}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1871850{,}550\ldots \\1000x & 18718{,}505\ldots \\\hline99000x & 1853132,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1853132}{99000}= \dfrac{463283}{24750}\)
10. \(x = 12,532\textbf{87}\textbf{87}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1253287{,}8787\ldots \\1000x & 12532{,}8787\ldots \\\hline99000x & 1240755,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1240755}{99000}= \dfrac{82717}{6600}\)
11. \(x = 1,\textbf{70}\textbf{70}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 170{,}770\ldots \\1x & 1{,}707\ldots \\\hline99x & 169,0000\ldots \end{array}\Leftrightarrow x = \dfrac{169}{99}\)
12. \(x = 17,972\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 179728{,}88\ldots \\1000x & 17972{,}88\ldots \\\hline9000x & 161756,00\ldots \end{array}\Leftrightarrow x = \dfrac{161756}{9000}= \dfrac{40439}{2250}\)