Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(-9,8\)
2. \(5,2\)
3. \(16,1010\ldots\)
4. \(4,51\)
5. \(9,99\ldots\)
6. \(17,524\)
7. \(17,7070\ldots\)
8. \(14,48644\ldots\)
9. \(20,946161\ldots\)
10. \(-10,506\)
11. \(11,1388\ldots\)
12. \(0,822\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(-9,8=\dfrac{-98}{10}=\dfrac{-49}{5}\)
2. \(5,2=\dfrac{52}{10}=\dfrac{26}{5}\)
3. \(x = 16,\textbf{10}\textbf{10}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1610{,}110\ldots \\1x & 16{,}101\ldots \\\hline99x & 1594,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1594}{99}\)
4. \(4,51=\dfrac{451}{100}\)
5. \(x = 9,\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 99{,}99\ldots \\1x & 9{,}99\ldots \\\hline9x & 90,00\ldots \end{array}\Leftrightarrow x = \dfrac{90}{9}= \dfrac{10}{1}\)
6. \(17,524=\dfrac{17524}{1000}=\dfrac{4381}{250}\)
7. \(x = 17,\textbf{70}\textbf{70}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1770{,}770\ldots \\1x & 17{,}707\ldots \\\hline99x & 1753,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1753}{99}\)
8. \(x = 14,486\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 144864{,}44\ldots \\1000x & 14486{,}44\ldots \\\hline9000x & 130378,00\ldots \end{array}\Leftrightarrow x = \dfrac{130378}{9000}= \dfrac{65189}{4500}\)
9. \(x = 20,94\textbf{61}\textbf{61}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 209461{,}6161\ldots \\100x & 2094{,}6161\ldots \\\hline9900x & 207367,0000\ldots \end{array}\Leftrightarrow x = \dfrac{207367}{9900}\)
10. \(-10,506=\dfrac{-10506}{1000}=\dfrac{-5253}{500}\)
11. \(x = 11,13\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 11138{,}88\ldots \\100x & 1113{,}88\ldots \\\hline900x & 10025,00\ldots \end{array}\Leftrightarrow x = \dfrac{10025}{900}= \dfrac{401}{36}\)
12. \(x = 0,8\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 82{,}22\ldots \\10x & 8{,}22\ldots \\\hline90x & 74,00\ldots \end{array}\Leftrightarrow x = \dfrac{74}{90}= \dfrac{37}{45}\)