Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(-11,67\)
2. \(20,9756767\ldots\)
3. \(15,84747\ldots\)
4. \(8,79090\ldots\)
5. \(16,9\)
6. \(10,5011\ldots\)
7. \(15,71692692\ldots\)
8. \(1,5934934\ldots\)
9. \(17,655\ldots\)
10. \(8,35353\ldots\)
11. \(13,4677\ldots\)
12. \(10,7\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(-11,67=\dfrac{-1167}{100}\)
2. \(x = 20,975\textbf{67}\textbf{67}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 2097567{,}6767\ldots \\1000x & 20975{,}6767\ldots \\\hline99000x & 2076592,0000\ldots \end{array}\Leftrightarrow x = \dfrac{2076592}{99000}= \dfrac{259574}{12375}\)
3. \(x = 15,8\textbf{47}\textbf{47}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 15847{,}4747\ldots \\10x & 158{,}4747\ldots \\\hline990x & 15689,0000\ldots \end{array}\Leftrightarrow x = \dfrac{15689}{990}\)
4. \(x = 8,7\textbf{90}\textbf{90}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 8790{,}990\ldots \\10x & 87{,}909\ldots \\\hline990x & 8703,0000\ldots \end{array}\Leftrightarrow x = \dfrac{8703}{990}= \dfrac{967}{110}\)
5. \(16,9=\dfrac{169}{10}\)
6. \(x = 10,50\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 10501{,}11\ldots \\100x & 1050{,}11\ldots \\\hline900x & 9451,00\ldots \end{array}\Leftrightarrow x = \dfrac{9451}{900}\)
7. \(x = 15,71\textbf{692}\textbf{692}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1571692{,}692692\ldots \\100x & 1571{,}692692\ldots \\\hline99900x & 1570121,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1570121}{99900}\)
8. \(x = 1,5\textbf{934}\textbf{934}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 15934{,}934934\ldots \\10x & 15{,}934934\ldots \\\hline9990x & 15919,000000\ldots \end{array}\Leftrightarrow x = \dfrac{15919}{9990}\)
9. \(x = 17,6\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1765{,}55\ldots \\10x & 176{,}55\ldots \\\hline90x & 1589,00\ldots \end{array}\Leftrightarrow x = \dfrac{1589}{90}\)
10. \(x = 8,3\textbf{53}\textbf{53}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 8353{,}5353\ldots \\10x & 83{,}5353\ldots \\\hline990x & 8270,0000\ldots \end{array}\Leftrightarrow x = \dfrac{8270}{990}= \dfrac{827}{99}\)
11. \(x = 13,46\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 13467{,}77\ldots \\100x & 1346{,}77\ldots \\\hline900x & 12121,00\ldots \end{array}\Leftrightarrow x = \dfrac{12121}{900}\)
12. \(10,7=\dfrac{107}{10}\)