Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(-17,54\)
2. \(16,13470470\ldots\)
3. \(12,837\)
4. \(7,13\)
5. \(-18,500\)
6. \(13,644\ldots\)
7. \(18,2525\ldots\)
8. \(12,1811\ldots\)
9. \(16,946946\ldots\)
10. \(13,66\ldots\)
11. \(8,465\)
12. \(17,54855\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(-17,54=\dfrac{-1754}{100}=\dfrac{-877}{50}\)
2. \(x = 16,13\textbf{470}\textbf{470}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1613470,47470\ldots \\100x & 1613,47047\ldots \\\hline99900x & 1611857,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1611857}{99900}\)
3. \(12,837=\dfrac{12837}{1000}\)
4. \(7,13=\dfrac{713}{100}\)
5. \(-18,500=\dfrac{-18500}{1000}=\dfrac{-37}{2}\)
6. \(x = 13,6\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1364,44\ldots \\10x & 136,44\ldots \\\hline90x & 1228,00\ldots \end{array}\Leftrightarrow x = \dfrac{1228}{90}= \dfrac{614}{45}\)
7. \(x = 18,\textbf{25}\textbf{25}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1825,2525\ldots \\1x & 18,2525\ldots \\\hline99x & 1807,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1807}{99}\)
8. \(x = 12,18\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 12181,11\ldots \\100x & 1218,11\ldots \\\hline900x & 10963,00\ldots \end{array}\Leftrightarrow x = \dfrac{10963}{900}\)
9. \(x = 16,\textbf{946}\textbf{946}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 16946,946946\ldots \\1x & 16,946946\ldots \\\hline999x & 16930,000000\ldots \end{array}\Leftrightarrow x = \dfrac{16930}{999}\)
10. \(x = 13,\textbf{6}\textbf{6}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 136,66\ldots \\1x & 13,66\ldots \\\hline9x & 123,00\ldots \end{array}\Leftrightarrow x = \dfrac{123}{9}= \dfrac{41}{3}\)
11. \(8,465=\dfrac{8465}{1000}=\dfrac{1693}{200}\)
12. \(x = 17,548\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 175485,55\ldots \\1000x & 17548,55\ldots \\\hline9000x & 157937,00\ldots \end{array}\Leftrightarrow x = \dfrac{157937}{9000}\)