Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(20,4545\ldots\)
2. \(-3,61\)
3. \(6,55\ldots\)
4. \(5,4\)
5. \(5,3722\ldots\)
6. \(-6,7\)
7. \(17,58976976\ldots\)
8. \(-3,14\)
9. \(16,86\)
10. \(9,917\)
11. \(3,285\)
12. \(8,4646\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 20,\textbf{45}\textbf{45}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 2045{,}4545\ldots \\1x & 20{,}4545\ldots \\\hline99x & 2025,0000\ldots \end{array}\Leftrightarrow x = \dfrac{2025}{99}= \dfrac{225}{11}\)
2. \(-3,61=\dfrac{-361}{100}\)
3. \(x = 6,\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 65{,}55\ldots \\1x & 6{,}55\ldots \\\hline9x & 59,00\ldots \end{array}\Leftrightarrow x = \dfrac{59}{9}\)
4. \(5,4=\dfrac{54}{10}=\dfrac{27}{5}\)
5. \(x = 5,37\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 5372{,}22\ldots \\100x & 537{,}22\ldots \\\hline900x & 4835,00\ldots \end{array}\Leftrightarrow x = \dfrac{4835}{900}= \dfrac{967}{180}\)
6. \(-6,7=\dfrac{-67}{10}\)
7. \(x = 17,58\textbf{976}\textbf{976}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1758976{,}976976\ldots \\100x & 1758{,}976976\ldots \\\hline99900x & 1757218,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1757218}{99900}= \dfrac{878609}{49950}\)
8. \(-3,14=\dfrac{-314}{100}=\dfrac{-157}{50}\)
9. \(16,86=\dfrac{1686}{100}=\dfrac{843}{50}\)
10. \(9,917=\dfrac{9917}{1000}\)
11. \(3,285=\dfrac{3285}{1000}=\dfrac{657}{200}\)
12. \(x = 8,\textbf{46}\textbf{46}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 846{,}4646\ldots \\1x & 8{,}4646\ldots \\\hline99x & 838,0000\ldots \end{array}\Leftrightarrow x = \dfrac{838}{99}\)