Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(-15,29\)
2. \(11,3383383\ldots\)
3. \(-6,6\)
4. \(3,44\ldots\)
5. \(2,207\)
6. \(18,492\)
7. \(18,2689689\ldots\)
8. \(-20,65\)
9. \(6,1919\ldots\)
10. \(0,555\ldots\)
11. \(1,955\ldots\)
12. \(5,6\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(-15,29=\dfrac{-1529}{100}\)
2. \(x = 11,3\textbf{383}\textbf{383}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 113383{,}383383\ldots \\10x & 113{,}383383\ldots \\\hline9990x & 113270,000000\ldots \end{array}\Leftrightarrow x = \dfrac{113270}{9990}= \dfrac{11327}{999}\)
3. \(-6,6=\dfrac{-66}{10}=\dfrac{-33}{5}\)
4. \(x = 3,\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 34{,}44\ldots \\1x & 3{,}44\ldots \\\hline9x & 31,00\ldots \end{array}\Leftrightarrow x = \dfrac{31}{9}\)
5. \(2,207=\dfrac{2207}{1000}\)
6. \(18,492=\dfrac{18492}{1000}=\dfrac{4623}{250}\)
7. \(x = 18,2\textbf{689}\textbf{689}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 182689{,}689689\ldots \\10x & 182{,}689689\ldots \\\hline9990x & 182507,000000\ldots \end{array}\Leftrightarrow x = \dfrac{182507}{9990}\)
8. \(-20,65=\dfrac{-2065}{100}=\dfrac{-413}{20}\)
9. \(x = 6,\textbf{19}\textbf{19}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 619{,}1919\ldots \\1x & 6{,}1919\ldots \\\hline99x & 613,0000\ldots \end{array}\Leftrightarrow x = \dfrac{613}{99}\)
10. \(x = 0,5\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 55{,}55\ldots \\10x & 5{,}55\ldots \\\hline90x & 50,00\ldots \end{array}\Leftrightarrow x = \dfrac{50}{90}= \dfrac{5}{9}\)
11. \(x = 1,9\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 195{,}55\ldots \\10x & 19{,}55\ldots \\\hline90x & 176,00\ldots \end{array}\Leftrightarrow x = \dfrac{176}{90}= \dfrac{88}{45}\)
12. \(5,6=\dfrac{56}{10}=\dfrac{28}{5}\)