Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(8,530\)
2. \(7,4955\ldots\)
3. \(-8,267\)
4. \(-16,71\)
5. \(-9,22\)
6. \(18,34242\ldots\)
7. \(-1,123\)
8. \(5,3833\ldots\)
9. \(12,88\ldots\)
10. \(20,499\ldots\)
11. \(-6,97\)
12. \(16,9\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(8,530=\dfrac{8530}{1000}=\dfrac{853}{100}\)
2. \(x = 7,49\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 7495{,}55\ldots \\100x & 749{,}55\ldots \\\hline900x & 6746,00\ldots \end{array}\Leftrightarrow x = \dfrac{6746}{900}= \dfrac{3373}{450}\)
3. \(-8,267=\dfrac{-8267}{1000}\)
4. \(-16,71=\dfrac{-1671}{100}\)
5. \(-9,22=\dfrac{-922}{100}=\dfrac{-461}{50}\)
6. \(x = 18,3\textbf{42}\textbf{42}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 18342{,}4242\ldots \\10x & 183{,}4242\ldots \\\hline990x & 18159,0000\ldots \end{array}\Leftrightarrow x = \dfrac{18159}{990}= \dfrac{6053}{330}\)
7. \(-1,123=\dfrac{-1123}{1000}\)
8. \(x = 5,38\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 5383{,}33\ldots \\100x & 538{,}33\ldots \\\hline900x & 4845,00\ldots \end{array}\Leftrightarrow x = \dfrac{4845}{900}= \dfrac{323}{60}\)
9. \(x = 12,\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 128{,}88\ldots \\1x & 12{,}88\ldots \\\hline9x & 116,00\ldots \end{array}\Leftrightarrow x = \dfrac{116}{9}\)
10. \(x = 20,4\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 2049{,}99\ldots \\10x & 204{,}99\ldots \\\hline90x & 1845,00\ldots \end{array}\Leftrightarrow x = \dfrac{1845}{90}= \dfrac{41}{2}\)
11. \(-6,97=\dfrac{-697}{100}\)
12. \(16,9=\dfrac{169}{10}\)