Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(1,6\)
2. \(17,833\ldots\)
3. \(0,355\ldots\)
4. \(4,8\)
5. \(1,27878\ldots\)
6. \(7,455\ldots\)
7. \(9,8\)
8. \(-5,4\)
9. \(11,6060\ldots\)
10. \(12,93\)
11. \(3,444\ldots\)
12. \(19,6932932\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(1,6=\dfrac{16}{10}=\dfrac{8}{5}\)
2. \(x = 17,8\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1783{,}33\ldots \\10x & 178{,}33\ldots \\\hline90x & 1605,00\ldots \end{array}\Leftrightarrow x = \dfrac{1605}{90}= \dfrac{107}{6}\)
3. \(x = 0,3\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 35{,}55\ldots \\10x & 3{,}55\ldots \\\hline90x & 32,00\ldots \end{array}\Leftrightarrow x = \dfrac{32}{90}= \dfrac{16}{45}\)
4. \(4,8=\dfrac{48}{10}=\dfrac{24}{5}\)
5. \(x = 1,2\textbf{78}\textbf{78}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 1278{,}7878\ldots \\10x & 12{,}7878\ldots \\\hline990x & 1266,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1266}{990}= \dfrac{211}{165}\)
6. \(x = 7,4\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 745{,}55\ldots \\10x & 74{,}55\ldots \\\hline90x & 671,00\ldots \end{array}\Leftrightarrow x = \dfrac{671}{90}\)
7. \(9,8=\dfrac{98}{10}=\dfrac{49}{5}\)
8. \(-5,4=\dfrac{-54}{10}=\dfrac{-27}{5}\)
9. \(x = 11,\textbf{60}\textbf{60}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1160{,}660\ldots \\1x & 11{,}606\ldots \\\hline99x & 1149,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1149}{99}= \dfrac{383}{33}\)
10. \(12,93=\dfrac{1293}{100}\)
11. \(x = 3,4\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 344{,}44\ldots \\10x & 34{,}44\ldots \\\hline90x & 310,00\ldots \end{array}\Leftrightarrow x = \dfrac{310}{90}= \dfrac{31}{9}\)
12. \(x = 19,6\textbf{932}\textbf{932}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 196932{,}932932\ldots \\10x & 196{,}932932\ldots \\\hline9990x & 196736,000000\ldots \end{array}\Leftrightarrow x = \dfrac{196736}{9990}= \dfrac{98368}{4995}\)