Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(20,505\)
2. \(11,3378378\ldots\)
3. \(1,7510510\ldots\)
4. \(17,6\)
5. \(10,88\ldots\)
6. \(19,884040\ldots\)
7. \(17,4356356\ldots\)
8. \(-17,3\)
9. \(-6,826\)
10. \(5,33\)
11. \(19,145\)
12. \(12,60\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(20,505=\dfrac{20505}{1000}=\dfrac{4101}{200}\)
2. \(x = 11,3\textbf{378}\textbf{378}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 113378{,}378378\ldots \\10x & 113{,}378378\ldots \\\hline9990x & 113265,000000\ldots \end{array}\Leftrightarrow x = \dfrac{113265}{9990}= \dfrac{839}{74}\)
3. \(x = 1,7\textbf{510}\textbf{510}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 17510{,}51510\ldots \\10x & 17{,}51051\ldots \\\hline9990x & 17493,000000\ldots \end{array}\Leftrightarrow x = \dfrac{17493}{9990}= \dfrac{5831}{3330}\)
4. \(17,6=\dfrac{176}{10}=\dfrac{88}{5}\)
5. \(x = 10,\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 108{,}88\ldots \\1x & 10{,}88\ldots \\\hline9x & 98,00\ldots \end{array}\Leftrightarrow x = \dfrac{98}{9}\)
6. \(x = 19,88\textbf{40}\textbf{40}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 198840{,}440\ldots \\100x & 1988{,}404\ldots \\\hline9900x & 196852,0000\ldots \end{array}\Leftrightarrow x = \dfrac{196852}{9900}= \dfrac{49213}{2475}\)
7. \(x = 17,4\textbf{356}\textbf{356}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 174356{,}356356\ldots \\10x & 174{,}356356\ldots \\\hline9990x & 174182,000000\ldots \end{array}\Leftrightarrow x = \dfrac{174182}{9990}= \dfrac{87091}{4995}\)
8. \(-17,3=\dfrac{-173}{10}\)
9. \(-6,826=\dfrac{-6826}{1000}=\dfrac{-3413}{500}\)
10. \(5,33=\dfrac{533}{100}\)
11. \(19,145=\dfrac{19145}{1000}=\dfrac{3829}{200}\)
12. \(12,60=\dfrac{1260}{100}=\dfrac{63}{5}\)