Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(13,85757\ldots\)
2. \(7,82\)
3. \(-1,5\)
4. \(1,808080\ldots\)
5. \(2,4451212\ldots\)
6. \(13,88\ldots\)
7. \(9,532\)
8. \(8,16877\ldots\)
9. \(18,711\)
10. \(-8,198\)
11. \(2,57899\ldots\)
12. \(2,849849\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 13,8\textbf{57}\textbf{57}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 13857{,}5757\ldots \\10x & 138{,}5757\ldots \\\hline990x & 13719,0000\ldots \end{array}\Leftrightarrow x = \dfrac{13719}{990}= \dfrac{4573}{330}\)
2. \(7,82=\dfrac{782}{100}=\dfrac{391}{50}\)
3. \(-1,5=\dfrac{-15}{10}=\dfrac{-3}{2}\)
4. \(x = 1,80\textbf{80}\textbf{80}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 18080{,}880\ldots \\100x & 180{,}808\ldots \\\hline9900x & 17900,0000\ldots \end{array}\Leftrightarrow x = \dfrac{17900}{9900}= \dfrac{179}{99}\)
5. \(x = 2,445\textbf{12}\textbf{12}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 244512{,}1212\ldots \\1000x & 2445{,}1212\ldots \\\hline99000x & 242067,0000\ldots \end{array}\Leftrightarrow x = \dfrac{242067}{99000}= \dfrac{80689}{33000}\)
6. \(x = 13,\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 138{,}88\ldots \\1x & 13{,}88\ldots \\\hline9x & 125,00\ldots \end{array}\Leftrightarrow x = \dfrac{125}{9}\)
7. \(9,532=\dfrac{9532}{1000}=\dfrac{2383}{250}\)
8. \(x = 8,168\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 81687{,}77\ldots \\1000x & 8168{,}77\ldots \\\hline9000x & 73519,00\ldots \end{array}\Leftrightarrow x = \dfrac{73519}{9000}\)
9. \(18,711=\dfrac{18711}{1000}\)
10. \(-8,198=\dfrac{-8198}{1000}=\dfrac{-4099}{500}\)
11. \(x = 2,578\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 25789{,}99\ldots \\1000x & 2578{,}99\ldots \\\hline9000x & 23211,00\ldots \end{array}\Leftrightarrow x = \dfrac{23211}{9000}= \dfrac{2579}{1000}\)
12. \(x = 2,\textbf{849}\textbf{849}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 2849{,}849849\ldots \\1x & 2{,}849849\ldots \\\hline999x & 2847,000000\ldots \end{array}\Leftrightarrow x = \dfrac{2847}{999}= \dfrac{949}{333}\)