Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(6,95131131\ldots\)
2. \(13,798798\ldots\)
3. \(-20,819\)
4. \(-8,83\)
5. \(18,12136136\ldots\)
6. \(9,55434434\ldots\)
7. \(19,22\ldots\)
8. \(-20,924\)
9. \(-15,5\)
10. \(11,617617\ldots\)
11. \(7,1666\ldots\)
12. \(20,813939\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 6,95\textbf{131}\textbf{131}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 695131{,}131131\ldots \\100x & 695{,}131131\ldots \\\hline99900x & 694436,000000\ldots \end{array}\Leftrightarrow x = \dfrac{694436}{99900}= \dfrac{173609}{24975}\)
2. \(x = 13,\textbf{798}\textbf{798}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 13798{,}798798\ldots \\1x & 13{,}798798\ldots \\\hline999x & 13785,000000\ldots \end{array}\Leftrightarrow x = \dfrac{13785}{999}= \dfrac{4595}{333}\)
3. \(-20,819=\dfrac{-20819}{1000}\)
4. \(-8,83=\dfrac{-883}{100}\)
5. \(x = 18,12\textbf{136}\textbf{136}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1812136{,}136136\ldots \\100x & 1812{,}136136\ldots \\\hline99900x & 1810324,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1810324}{99900}= \dfrac{452581}{24975}\)
6. \(x = 9,55\textbf{434}\textbf{434}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 955434{,}434434\ldots \\100x & 955{,}434434\ldots \\\hline99900x & 954479,000000\ldots \end{array}\Leftrightarrow x = \dfrac{954479}{99900}\)
7. \(x = 19,\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 192{,}22\ldots \\1x & 19{,}22\ldots \\\hline9x & 173,00\ldots \end{array}\Leftrightarrow x = \dfrac{173}{9}\)
8. \(-20,924=\dfrac{-20924}{1000}=\dfrac{-5231}{250}\)
9. \(-15,5=\dfrac{-155}{10}=\dfrac{-31}{2}\)
10. \(x = 11,\textbf{617}\textbf{617}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 11617{,}617617\ldots \\1x & 11{,}617617\ldots \\\hline999x & 11606,000000\ldots \end{array}\Leftrightarrow x = \dfrac{11606}{999}\)
11. \(x = 7,16\textbf{6}\textbf{6}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 7166{,}66\ldots \\100x & 716{,}66\ldots \\\hline900x & 6450,00\ldots \end{array}\Leftrightarrow x = \dfrac{6450}{900}= \dfrac{43}{6}\)
12. \(x = 20,81\textbf{39}\textbf{39}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 208139{,}3939\ldots \\100x & 2081{,}3939\ldots \\\hline9900x & 206058,0000\ldots \end{array}\Leftrightarrow x = \dfrac{206058}{9900}= \dfrac{34343}{1650}\)