Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(12,2431431\ldots\)
2. \(3,7518787\ldots\)
3. \(20,77\ldots\)
4. \(19,8\)
5. \(15,61133\ldots\)
6. \(-17,69\)
7. \(2,411\ldots\)
8. \(18,7\)
9. \(11,4\)
10. \(11,786\)
11. \(-14,410\)
12. \(14,76\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 12,2\textbf{431}\textbf{431}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 122431{,}431431\ldots \\10x & 122{,}431431\ldots \\\hline9990x & 122309,000000\ldots \end{array}\Leftrightarrow x = \dfrac{122309}{9990}\)
2. \(x = 3,751\textbf{87}\textbf{87}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 375187{,}8787\ldots \\1000x & 3751{,}8787\ldots \\\hline99000x & 371436,0000\ldots \end{array}\Leftrightarrow x = \dfrac{371436}{99000}= \dfrac{30953}{8250}\)
3. \(x = 20,\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 207{,}77\ldots \\1x & 20{,}77\ldots \\\hline9x & 187,00\ldots \end{array}\Leftrightarrow x = \dfrac{187}{9}\)
4. \(19,8=\dfrac{198}{10}=\dfrac{99}{5}\)
5. \(x = 15,611\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 156113{,}33\ldots \\1000x & 15611{,}33\ldots \\\hline9000x & 140502,00\ldots \end{array}\Leftrightarrow x = \dfrac{140502}{9000}= \dfrac{23417}{1500}\)
6. \(-17,69=\dfrac{-1769}{100}\)
7. \(x = 2,4\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 241{,}11\ldots \\10x & 24{,}11\ldots \\\hline90x & 217,00\ldots \end{array}\Leftrightarrow x = \dfrac{217}{90}\)
8. \(18,7=\dfrac{187}{10}\)
9. \(11,4=\dfrac{114}{10}=\dfrac{57}{5}\)
10. \(11,786=\dfrac{11786}{1000}=\dfrac{5893}{500}\)
11. \(-14,410=\dfrac{-14410}{1000}=\dfrac{-1441}{100}\)
12. \(14,76=\dfrac{1476}{100}=\dfrac{369}{25}\)