Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(20,41\)
2. \(4,233\)
3. \(-11,59\)
4. \(18,171171\ldots\)
5. \(7,5945945\ldots\)
6. \(5,6091212\ldots\)
7. \(-1,10\)
8. \(7,22\ldots\)
9. \(15,51640640\ldots\)
10. \(18,899\ldots\)
11. \(16,210\)
12. \(14,76161\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(20,41=\dfrac{2041}{100}\)
2. \(4,233=\dfrac{4233}{1000}\)
3. \(-11,59=\dfrac{-1159}{100}\)
4. \(x = 18,\textbf{171}\textbf{171}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 18171{,}171171\ldots \\1x & 18{,}171171\ldots \\\hline999x & 18153,000000\ldots \end{array}\Leftrightarrow x = \dfrac{18153}{999}= \dfrac{2017}{111}\)
5. \(x = 7,5\textbf{945}\textbf{945}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 75945{,}945945\ldots \\10x & 75{,}945945\ldots \\\hline9990x & 75870,000000\ldots \end{array}\Leftrightarrow x = \dfrac{75870}{9990}= \dfrac{281}{37}\)
6. \(x = 5,609\textbf{12}\textbf{12}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 560912{,}1212\ldots \\1000x & 5609{,}1212\ldots \\\hline99000x & 555303,0000\ldots \end{array}\Leftrightarrow x = \dfrac{555303}{99000}= \dfrac{185101}{33000}\)
7. \(-1,10=\dfrac{-110}{100}=\dfrac{-11}{10}\)
8. \(x = 7,\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 72{,}22\ldots \\1x & 7{,}22\ldots \\\hline9x & 65,00\ldots \end{array}\Leftrightarrow x = \dfrac{65}{9}\)
9. \(x = 15,51\textbf{640}\textbf{640}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1551640{,}64640\ldots \\100x & 1551{,}64064\ldots \\\hline99900x & 1550089,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1550089}{99900}\)
10. \(x = 18,8\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1889{,}99\ldots \\10x & 188{,}99\ldots \\\hline90x & 1701,00\ldots \end{array}\Leftrightarrow x = \dfrac{1701}{90}= \dfrac{189}{10}\)
11. \(16,210=\dfrac{16210}{1000}=\dfrac{1621}{100}\)
12. \(x = 14,7\textbf{61}\textbf{61}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 14761{,}6161\ldots \\10x & 147{,}6161\ldots \\\hline990x & 14614,0000\ldots \end{array}\Leftrightarrow x = \dfrac{14614}{990}= \dfrac{7307}{495}\)