Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(12,69\)
2. \(14,1333\ldots\)
3. \(11,5999\ldots\)
4. \(16,798\)
5. \(3,62\)
6. \(10,5\)
7. \(17,6\)
8. \(0,429429\ldots\)
9. \(12,9\)
10. \(5,477\ldots\)
11. \(6,87269269\ldots\)
12. \(10,33\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(12,69=\dfrac{1269}{100}\)
2. \(x = 14,13\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 14133{,}33\ldots \\100x & 1413{,}33\ldots \\\hline900x & 12720,00\ldots \end{array}\Leftrightarrow x = \dfrac{12720}{900}= \dfrac{212}{15}\)
3. \(x = 11,59\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 11599{,}99\ldots \\100x & 1159{,}99\ldots \\\hline900x & 10440,00\ldots \end{array}\Leftrightarrow x = \dfrac{10440}{900}= \dfrac{58}{5}\)
4. \(16,798=\dfrac{16798}{1000}=\dfrac{8399}{500}\)
5. \(3,62=\dfrac{362}{100}=\dfrac{181}{50}\)
6. \(10,5=\dfrac{105}{10}=\dfrac{21}{2}\)
7. \(17,6=\dfrac{176}{10}=\dfrac{88}{5}\)
8. \(x = 0,\textbf{429}\textbf{429}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 429{,}429429\ldots \\1x & 0{,}429429\ldots \\\hline999x & 429,000000\ldots \end{array}\Leftrightarrow x = \dfrac{429}{999}= \dfrac{143}{333}\)
9. \(12,9=\dfrac{129}{10}\)
10. \(x = 5,4\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 547{,}77\ldots \\10x & 54{,}77\ldots \\\hline90x & 493,00\ldots \end{array}\Leftrightarrow x = \dfrac{493}{90}\)
11. \(x = 6,87\textbf{269}\textbf{269}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 687269{,}269269\ldots \\100x & 687{,}269269\ldots \\\hline99900x & 686582,000000\ldots \end{array}\Leftrightarrow x = \dfrac{686582}{99900}= \dfrac{343291}{49950}\)
12. \(x = 10,\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 103{,}33\ldots \\1x & 10{,}33\ldots \\\hline9x & 93,00\ldots \end{array}\Leftrightarrow x = \dfrac{93}{9}= \dfrac{31}{3}\)