Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(-11,92\)
2. \(-2,2\)
3. \(-1,262\)
4. \(20,541010\ldots\)
5. \(9,876876\ldots\)
6. \(16,52599\ldots\)
7. \(3,406\)
8. \(-2,30\)
9. \(18,7878\ldots\)
10. \(3,21361361\ldots\)
11. \(15,36\)
12. \(6,7676\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(-11,92=\dfrac{-1192}{100}=\dfrac{-298}{25}\)
2. \(-2,2=\dfrac{-22}{10}=\dfrac{-11}{5}\)
3. \(-1,262=\dfrac{-1262}{1000}=\dfrac{-631}{500}\)
4. \(x = 20,54\textbf{10}\textbf{10}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 205410,110\ldots \\100x & 2054,101\ldots \\\hline9900x & 203356,0000\ldots \end{array}\Leftrightarrow x = \dfrac{203356}{9900}= \dfrac{50839}{2475}\)
5. \(x = 9,\textbf{876}\textbf{876}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 9876,876876\ldots \\1x & 9,876876\ldots \\\hline999x & 9867,000000\ldots \end{array}\Leftrightarrow x = \dfrac{9867}{999}= \dfrac{3289}{333}\)
6. \(x = 16,525\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 165259,99\ldots \\1000x & 16525,99\ldots \\\hline9000x & 148734,00\ldots \end{array}\Leftrightarrow x = \dfrac{148734}{9000}= \dfrac{8263}{500}\)
7. \(3,406=\dfrac{3406}{1000}=\dfrac{1703}{500}\)
8. \(-2,30=\dfrac{-230}{100}=\dfrac{-23}{10}\)
9. \(x = 18,\textbf{78}\textbf{78}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1878,7878\ldots \\1x & 18,7878\ldots \\\hline99x & 1860,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1860}{99}= \dfrac{620}{33}\)
10. \(x = 3,21\textbf{361}\textbf{361}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 321361,361361\ldots \\100x & 321,361361\ldots \\\hline99900x & 321040,000000\ldots \end{array}\Leftrightarrow x = \dfrac{321040}{99900}= \dfrac{16052}{4995}\)
11. \(15,36=\dfrac{1536}{100}=\dfrac{384}{25}\)
12. \(x = 6,\textbf{76}\textbf{76}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 676,7676\ldots \\1x & 6,7676\ldots \\\hline99x & 670,0000\ldots \end{array}\Leftrightarrow x = \dfrac{670}{99}\)