Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(10,22\ldots\)
2. \(20,2622\ldots\)
3. \(9,4\)
4. \(10,484\)
5. \(4,552782782\ldots\)
6. \(11,3\)
7. \(-3,9\)
8. \(16,86161\ldots\)
9. \(7,3\)
10. \(14,78836836\ldots\)
11. \(-11,5\)
12. \(11,695\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 10,\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 102{,}22\ldots \\1x & 10{,}22\ldots \\\hline9x & 92,00\ldots \end{array}\Leftrightarrow x = \dfrac{92}{9}\)
2. \(x = 20,26\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 20262{,}22\ldots \\100x & 2026{,}22\ldots \\\hline900x & 18236,00\ldots \end{array}\Leftrightarrow x = \dfrac{18236}{900}= \dfrac{4559}{225}\)
3. \(9,4=\dfrac{94}{10}=\dfrac{47}{5}\)
4. \(10,484=\dfrac{10484}{1000}=\dfrac{2621}{250}\)
5. \(x = 4,552\textbf{782}\textbf{782}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 4552782{,}782782\ldots \\1000x & 4552{,}782782\ldots \\\hline999000x & 4548230,000000\ldots \end{array}\Leftrightarrow x = \dfrac{4548230}{999000}= \dfrac{454823}{99900}\)
6. \(11,3=\dfrac{113}{10}\)
7. \(-3,9=\dfrac{-39}{10}\)
8. \(x = 16,8\textbf{61}\textbf{61}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 16861{,}6161\ldots \\10x & 168{,}6161\ldots \\\hline990x & 16693,0000\ldots \end{array}\Leftrightarrow x = \dfrac{16693}{990}\)
9. \(7,3=\dfrac{73}{10}\)
10. \(x = 14,78\textbf{836}\textbf{836}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1478836{,}836836\ldots \\100x & 1478{,}836836\ldots \\\hline99900x & 1477358,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1477358}{99900}= \dfrac{738679}{49950}\)
11. \(-11,5=\dfrac{-115}{10}=\dfrac{-23}{2}\)
12. \(11,695=\dfrac{11695}{1000}=\dfrac{2339}{200}\)