Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(16,704704\ldots\)
2. \(15,9353636\ldots\)
3. \(-10,62\)
4. \(0,83232\ldots\)
5. \(7,3555454\ldots\)
6. \(18,33\)
7. \(11,999\)
8. \(-7,5\)
9. \(17,209191\ldots\)
10. \(11,8833\ldots\)
11. \(-9,8\)
12. \(2,77\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 16,\textbf{704}\textbf{704}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 16704{,}704704\ldots \\1x & 16{,}704704\ldots \\\hline999x & 16688,000000\ldots \end{array}\Leftrightarrow x = \dfrac{16688}{999}\)
2. \(x = 15,935\textbf{36}\textbf{36}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1593536{,}3636\ldots \\1000x & 15935{,}3636\ldots \\\hline99000x & 1577601,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1577601}{99000}= \dfrac{175289}{11000}\)
3. \(-10,62=\dfrac{-1062}{100}=\dfrac{-531}{50}\)
4. \(x = 0,8\textbf{32}\textbf{32}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 832{,}3232\ldots \\10x & 8{,}3232\ldots \\\hline990x & 824,0000\ldots \end{array}\Leftrightarrow x = \dfrac{824}{990}= \dfrac{412}{495}\)
5. \(x = 7,355\textbf{54}\textbf{54}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 735554{,}5454\ldots \\1000x & 7355{,}5454\ldots \\\hline99000x & 728199,0000\ldots \end{array}\Leftrightarrow x = \dfrac{728199}{99000}= \dfrac{80911}{11000}\)
6. \(18,33=\dfrac{1833}{100}\)
7. \(11,999=\dfrac{11999}{1000}\)
8. \(-7,5=\dfrac{-75}{10}=\dfrac{-15}{2}\)
9. \(x = 17,20\textbf{91}\textbf{91}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 172091{,}9191\ldots \\100x & 1720{,}9191\ldots \\\hline9900x & 170371,0000\ldots \end{array}\Leftrightarrow x = \dfrac{170371}{9900}\)
10. \(x = 11,88\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 11883{,}33\ldots \\100x & 1188{,}33\ldots \\\hline900x & 10695,00\ldots \end{array}\Leftrightarrow x = \dfrac{10695}{900}= \dfrac{713}{60}\)
11. \(-9,8=\dfrac{-98}{10}=\dfrac{-49}{5}\)
12. \(2,77=\dfrac{277}{100}\)