Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(5,5766\ldots\)
2. \(-11,65\)
3. \(6,7\)
4. \(17,18\)
5. \(11,190\)
6. \(12,791\)
7. \(13,3756868\ldots\)
8. \(-20,7\)
9. \(18,44\)
10. \(18,179393\ldots\)
11. \(5,44\ldots\)
12. \(16,62525\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 5,57\textbf{6}\textbf{6}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 5576,66\ldots \\100x & 557,66\ldots \\\hline900x & 5019,00\ldots \end{array}\Leftrightarrow x = \dfrac{5019}{900}= \dfrac{1673}{300}\)
2. \(-11,65=\dfrac{-1165}{100}=\dfrac{-233}{20}\)
3. \(6,7=\dfrac{67}{10}\)
4. \(17,18=\dfrac{1718}{100}=\dfrac{859}{50}\)
5. \(11,190=\dfrac{11190}{1000}=\dfrac{1119}{100}\)
6. \(12,791=\dfrac{12791}{1000}\)
7. \(x = 13,375\textbf{68}\textbf{68}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1337568,6868\ldots \\1000x & 13375,6868\ldots \\\hline99000x & 1324193,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1324193}{99000}\)
8. \(-20,7=\dfrac{-207}{10}\)
9. \(18,44=\dfrac{1844}{100}=\dfrac{461}{25}\)
10. \(x = 18,17\textbf{93}\textbf{93}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 181793,9393\ldots \\100x & 1817,9393\ldots \\\hline9900x & 179976,0000\ldots \end{array}\Leftrightarrow x = \dfrac{179976}{9900}= \dfrac{14998}{825}\)
11. \(x = 5,\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 54,44\ldots \\1x & 5,44\ldots \\\hline9x & 49,00\ldots \end{array}\Leftrightarrow x = \dfrac{49}{9}\)
12. \(x = 16,6\textbf{25}\textbf{25}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 16625,2525\ldots \\10x & 166,2525\ldots \\\hline990x & 16459,0000\ldots \end{array}\Leftrightarrow x = \dfrac{16459}{990}\)