Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(9,4\)
2. \(12,6\)
3. \(20,539516516\ldots\)
4. \(7,477\ldots\)
5. \(19,51\)
6. \(-11,817\)
7. \(-2,9\)
8. \(6,55\ldots\)
9. \(-5,316\)
10. \(14,712712\ldots\)
11. \(-6,3\)
12. \(1,489\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(9,4=\dfrac{94}{10}=\dfrac{47}{5}\)
2. \(12,6=\dfrac{126}{10}=\dfrac{63}{5}\)
3. \(x = 20,539\textbf{516}\textbf{516}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 20539516,516516\ldots \\1000x & 20539,516516\ldots \\\hline999000x & 20518977,000000\ldots \end{array}\Leftrightarrow x = \dfrac{20518977}{999000}= \dfrac{6839659}{333000}\)
4. \(x = 7,4\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 747,77\ldots \\10x & 74,77\ldots \\\hline90x & 673,00\ldots \end{array}\Leftrightarrow x = \dfrac{673}{90}\)
5. \(19,51=\dfrac{1951}{100}\)
6. \(-11,817=\dfrac{-11817}{1000}\)
7. \(-2,9=\dfrac{-29}{10}\)
8. \(x = 6,\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 65,55\ldots \\1x & 6,55\ldots \\\hline9x & 59,00\ldots \end{array}\Leftrightarrow x = \dfrac{59}{9}\)
9. \(-5,316=\dfrac{-5316}{1000}=\dfrac{-1329}{250}\)
10. \(x = 14,\textbf{712}\textbf{712}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 14712,712712\ldots \\1x & 14,712712\ldots \\\hline999x & 14698,000000\ldots \end{array}\Leftrightarrow x = \dfrac{14698}{999}\)
11. \(-6,3=\dfrac{-63}{10}\)
12. \(1,489=\dfrac{1489}{1000}\)