Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(10,288\ldots\)
2. \(7,4\)
3. \(-1,7\)
4. \(13,652\)
5. \(15,90\)
6. \(4,4325252\ldots\)
7. \(-1,2\)
8. \(-11,3\)
9. \(18,22\ldots\)
10. \(9,781\)
11. \(-15,940\)
12. \(8,87474\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 10,2\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1028,88\ldots \\10x & 102,88\ldots \\\hline90x & 926,00\ldots \end{array}\Leftrightarrow x = \dfrac{926}{90}= \dfrac{463}{45}\)
2. \(7,4=\dfrac{74}{10}=\dfrac{37}{5}\)
3. \(-1,7=\dfrac{-17}{10}\)
4. \(13,652=\dfrac{13652}{1000}=\dfrac{3413}{250}\)
5. \(15,90=\dfrac{1590}{100}=\dfrac{159}{10}\)
6. \(x = 4,432\textbf{52}\textbf{52}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 443252,5252\ldots \\1000x & 4432,5252\ldots \\\hline99000x & 438820,0000\ldots \end{array}\Leftrightarrow x = \dfrac{438820}{99000}= \dfrac{21941}{4950}\)
7. \(-1,2=\dfrac{-12}{10}=\dfrac{-6}{5}\)
8. \(-11,3=\dfrac{-113}{10}\)
9. \(x = 18,\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 182,22\ldots \\1x & 18,22\ldots \\\hline9x & 164,00\ldots \end{array}\Leftrightarrow x = \dfrac{164}{9}\)
10. \(9,781=\dfrac{9781}{1000}\)
11. \(-15,940=\dfrac{-15940}{1000}=\dfrac{-797}{50}\)
12. \(x = 8,8\textbf{74}\textbf{74}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 8874,7474\ldots \\10x & 88,7474\ldots \\\hline990x & 8786,0000\ldots \end{array}\Leftrightarrow x = \dfrac{8786}{990}= \dfrac{4393}{495}\)