Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(-3,93\)
2. \(8,33\ldots\)
3. \(-2,770\)
4. \(10,77\ldots\)
5. \(15,5\)
6. \(-10,62\)
7. \(-13,782\)
8. \(17,88\ldots\)
9. \(18,9564564\ldots\)
10. \(18,60422\ldots\)
11. \(3,36573573\ldots\)
12. \(7,97434434\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(-3,93=\dfrac{-393}{100}\)
2. \(x = 8,\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 83,33\ldots \\1x & 8,33\ldots \\\hline9x & 75,00\ldots \end{array}\Leftrightarrow x = \dfrac{75}{9}= \dfrac{25}{3}\)
3. \(-2,770=\dfrac{-2770}{1000}=\dfrac{-277}{100}\)
4. \(x = 10,\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 107,77\ldots \\1x & 10,77\ldots \\\hline9x & 97,00\ldots \end{array}\Leftrightarrow x = \dfrac{97}{9}\)
5. \(15,5=\dfrac{155}{10}=\dfrac{31}{2}\)
6. \(-10,62=\dfrac{-1062}{100}=\dfrac{-531}{50}\)
7. \(-13,782=\dfrac{-13782}{1000}=\dfrac{-6891}{500}\)
8. \(x = 17,\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 178,88\ldots \\1x & 17,88\ldots \\\hline9x & 161,00\ldots \end{array}\Leftrightarrow x = \dfrac{161}{9}\)
9. \(x = 18,9\textbf{564}\textbf{564}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 189564,564564\ldots \\10x & 189,564564\ldots \\\hline9990x & 189375,000000\ldots \end{array}\Leftrightarrow x = \dfrac{189375}{9990}= \dfrac{12625}{666}\)
10. \(x = 18,604\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 186042,22\ldots \\1000x & 18604,22\ldots \\\hline9000x & 167438,00\ldots \end{array}\Leftrightarrow x = \dfrac{167438}{9000}= \dfrac{83719}{4500}\)
11. \(x = 3,36\textbf{573}\textbf{573}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 336573,573573\ldots \\100x & 336,573573\ldots \\\hline99900x & 336237,000000\ldots \end{array}\Leftrightarrow x = \dfrac{336237}{99900}= \dfrac{112079}{33300}\)
12. \(x = 7,97\textbf{434}\textbf{434}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 797434,434434\ldots \\100x & 797,434434\ldots \\\hline99900x & 796637,000000\ldots \end{array}\Leftrightarrow x = \dfrac{796637}{99900}\)