Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(1,399\ldots\)
2. \(-18,9\)
3. \(4,490723723\ldots\)
4. \(12,227\)
5. \(2,860482482\ldots\)
6. \(16,7618618\ldots\)
7. \(0,9534040\ldots\)
8. \(12,306767\ldots\)
9. \(10,322\ldots\)
10. \(19,6767\ldots\)
11. \(6,875\)
12. \(14,257575\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 1,3\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 139{,}99\ldots \\10x & 13{,}99\ldots \\\hline90x & 126,00\ldots \end{array}\Leftrightarrow x = \dfrac{126}{90}= \dfrac{7}{5}\)
2. \(-18,9=\dfrac{-189}{10}\)
3. \(x = 4,490\textbf{723}\textbf{723}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 4490723{,}723723\ldots \\1000x & 4490{,}723723\ldots \\\hline999000x & 4486233,000000\ldots \end{array}\Leftrightarrow x = \dfrac{4486233}{999000}= \dfrac{1495411}{333000}\)
4. \(12,227=\dfrac{12227}{1000}\)
5. \(x = 2,860\textbf{482}\textbf{482}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 2860482{,}482482\ldots \\1000x & 2860{,}482482\ldots \\\hline999000x & 2857622,000000\ldots \end{array}\Leftrightarrow x = \dfrac{2857622}{999000}= \dfrac{1428811}{499500}\)
6. \(x = 16,7\textbf{618}\textbf{618}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 167618{,}618618\ldots \\10x & 167{,}618618\ldots \\\hline9990x & 167451,000000\ldots \end{array}\Leftrightarrow x = \dfrac{167451}{9990}= \dfrac{55817}{3330}\)
7. \(x = 0,953\textbf{40}\textbf{40}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 95340{,}440\ldots \\1000x & 953{,}404\ldots \\\hline99000x & 94387,0000\ldots \end{array}\Leftrightarrow x = \dfrac{94387}{99000}\)
8. \(x = 12,30\textbf{67}\textbf{67}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 123067{,}6767\ldots \\100x & 1230{,}6767\ldots \\\hline9900x & 121837,0000\ldots \end{array}\Leftrightarrow x = \dfrac{121837}{9900}\)
9. \(x = 10,3\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1032{,}22\ldots \\10x & 103{,}22\ldots \\\hline90x & 929,00\ldots \end{array}\Leftrightarrow x = \dfrac{929}{90}\)
10. \(x = 19,\textbf{67}\textbf{67}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1967{,}6767\ldots \\1x & 19{,}6767\ldots \\\hline99x & 1948,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1948}{99}\)
11. \(6,875=\dfrac{6875}{1000}=\dfrac{55}{8}\)
12. \(x = 14,25\textbf{75}\textbf{75}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 142575{,}7575\ldots \\100x & 1425{,}7575\ldots \\\hline9900x & 141150,0000\ldots \end{array}\Leftrightarrow x = \dfrac{141150}{9900}= \dfrac{941}{66}\)