Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(8,253717717\ldots\)
2. \(13,343\)
3. \(18,94460460\ldots\)
4. \(5,57\)
5. \(1,384384\ldots\)
6. \(10,7698787\ldots\)
7. \(-17,379\)
8. \(14,823\)
9. \(10,350\)
10. \(13,522\ldots\)
11. \(11,922\ldots\)
12. \(14,89898\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 8,253\textbf{717}\textbf{717}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 8253717{,}717717\ldots \\1000x & 8253{,}717717\ldots \\\hline999000x & 8245464,000000\ldots \end{array}\Leftrightarrow x = \dfrac{8245464}{999000}= \dfrac{343561}{41625}\)
2. \(13,343=\dfrac{13343}{1000}\)
3. \(x = 18,94\textbf{460}\textbf{460}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1894460{,}46460\ldots \\100x & 1894{,}46046\ldots \\\hline99900x & 1892566,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1892566}{99900}= \dfrac{946283}{49950}\)
4. \(5,57=\dfrac{557}{100}\)
5. \(x = 1,\textbf{384}\textbf{384}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 1384{,}384384\ldots \\1x & 1{,}384384\ldots \\\hline999x & 1383,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1383}{999}= \dfrac{461}{333}\)
6. \(x = 10,769\textbf{87}\textbf{87}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1076987{,}8787\ldots \\1000x & 10769{,}8787\ldots \\\hline99000x & 1066218,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1066218}{99000}= \dfrac{177703}{16500}\)
7. \(-17,379=\dfrac{-17379}{1000}\)
8. \(14,823=\dfrac{14823}{1000}\)
9. \(10,350=\dfrac{10350}{1000}=\dfrac{207}{20}\)
10. \(x = 13,5\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1352{,}22\ldots \\10x & 135{,}22\ldots \\\hline90x & 1217,00\ldots \end{array}\Leftrightarrow x = \dfrac{1217}{90}\)
11. \(x = 11,9\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1192{,}22\ldots \\10x & 119{,}22\ldots \\\hline90x & 1073,00\ldots \end{array}\Leftrightarrow x = \dfrac{1073}{90}\)
12. \(x = 14,8\textbf{98}\textbf{98}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 14898{,}9898\ldots \\10x & 148{,}9898\ldots \\\hline990x & 14750,0000\ldots \end{array}\Leftrightarrow x = \dfrac{14750}{990}= \dfrac{1475}{99}\)