Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(4,9302020\ldots\)
2. \(4,6362323\ldots\)
3. \(4,170756756\ldots\)
4. \(20,17\)
5. \(1,7\)
6. \(8,9\)
7. \(17,7725725\ldots\)
8. \(4,1212\ldots\)
9. \(19,611\ldots\)
10. \(20,11\ldots\)
11. \(10,83824824\ldots\)
12. \(-20,9\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 4,930\textbf{20}\textbf{20}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 493020{,}220\ldots \\1000x & 4930{,}202\ldots \\\hline99000x & 488090,0000\ldots \end{array}\Leftrightarrow x = \dfrac{488090}{99000}= \dfrac{48809}{9900}\)
2. \(x = 4,636\textbf{23}\textbf{23}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 463623{,}2323\ldots \\1000x & 4636{,}2323\ldots \\\hline99000x & 458987,0000\ldots \end{array}\Leftrightarrow x = \dfrac{458987}{99000}\)
3. \(x = 4,170\textbf{756}\textbf{756}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 4170756{,}756756\ldots \\1000x & 4170{,}756756\ldots \\\hline999000x & 4166586,000000\ldots \end{array}\Leftrightarrow x = \dfrac{4166586}{999000}= \dfrac{77159}{18500}\)
4. \(20,17=\dfrac{2017}{100}\)
5. \(1,7=\dfrac{17}{10}\)
6. \(8,9=\dfrac{89}{10}\)
7. \(x = 17,7\textbf{725}\textbf{725}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 177725{,}725725\ldots \\10x & 177{,}725725\ldots \\\hline9990x & 177548,000000\ldots \end{array}\Leftrightarrow x = \dfrac{177548}{9990}= \dfrac{88774}{4995}\)
8. \(x = 4,\textbf{12}\textbf{12}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 412{,}1212\ldots \\1x & 4{,}1212\ldots \\\hline99x & 408,0000\ldots \end{array}\Leftrightarrow x = \dfrac{408}{99}= \dfrac{136}{33}\)
9. \(x = 19,6\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1961{,}11\ldots \\10x & 196{,}11\ldots \\\hline90x & 1765,00\ldots \end{array}\Leftrightarrow x = \dfrac{1765}{90}= \dfrac{353}{18}\)
10. \(x = 20,\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 201{,}11\ldots \\1x & 20{,}11\ldots \\\hline9x & 181,00\ldots \end{array}\Leftrightarrow x = \dfrac{181}{9}\)
11. \(x = 10,83\textbf{824}\textbf{824}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1083824{,}824824\ldots \\100x & 1083{,}824824\ldots \\\hline99900x & 1082741,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1082741}{99900}\)
12. \(-20,9=\dfrac{-209}{10}\)