Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(6,386386\ldots\)
2. \(-19,58\)
3. \(-10,994\)
4. \(5,7\)
5. \(4,488\ldots\)
6. \(4,8222\ldots\)
7. \(0,510280280\ldots\)
8. \(0,1515\ldots\)
9. \(9,8\)
10. \(1,3426426\ldots\)
11. \(19,58\)
12. \(1,22\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 6,\textbf{386}\textbf{386}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 6386{,}386386\ldots \\1x & 6{,}386386\ldots \\\hline999x & 6380,000000\ldots \end{array}\Leftrightarrow x = \dfrac{6380}{999}\)
2. \(-19,58=\dfrac{-1958}{100}=\dfrac{-979}{50}\)
3. \(-10,994=\dfrac{-10994}{1000}=\dfrac{-5497}{500}\)
4. \(5,7=\dfrac{57}{10}\)
5. \(x = 4,4\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 448{,}88\ldots \\10x & 44{,}88\ldots \\\hline90x & 404,00\ldots \end{array}\Leftrightarrow x = \dfrac{404}{90}= \dfrac{202}{45}\)
6. \(x = 4,82\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 4822{,}22\ldots \\100x & 482{,}22\ldots \\\hline900x & 4340,00\ldots \end{array}\Leftrightarrow x = \dfrac{4340}{900}= \dfrac{217}{45}\)
7. \(x = 0,510\textbf{280}\textbf{280}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 510280{,}28280\ldots \\1000x & 510{,}28028\ldots \\\hline999000x & 509770,000000\ldots \end{array}\Leftrightarrow x = \dfrac{509770}{999000}= \dfrac{50977}{99900}\)
8. \(x = 0,\textbf{15}\textbf{15}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 15{,}1515\ldots \\1x & 0{,}1515\ldots \\\hline99x & 15,0000\ldots \end{array}\Leftrightarrow x = \dfrac{15}{99}= \dfrac{5}{33}\)
9. \(9,8=\dfrac{98}{10}=\dfrac{49}{5}\)
10. \(x = 1,3\textbf{426}\textbf{426}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 13426{,}426426\ldots \\10x & 13{,}426426\ldots \\\hline9990x & 13413,000000\ldots \end{array}\Leftrightarrow x = \dfrac{13413}{9990}= \dfrac{4471}{3330}\)
11. \(19,58=\dfrac{1958}{100}=\dfrac{979}{50}\)
12. \(x = 1,\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 12{,}22\ldots \\1x & 1{,}22\ldots \\\hline9x & 11,00\ldots \end{array}\Leftrightarrow x = \dfrac{11}{9}\)