Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(15,198\)
2. \(16,11\ldots\)
3. \(8,6\)
4. \(10,288\ldots\)
5. \(-10,3\)
6. \(3,644\ldots\)
7. \(7,673717717\ldots\)
8. \(15,32\)
9. \(20,99\ldots\)
10. \(7,77\ldots\)
11. \(-3,896\)
12. \(-11,775\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(15,198=\dfrac{15198}{1000}=\dfrac{7599}{500}\)
2. \(x = 16,\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 161{,}11\ldots \\1x & 16{,}11\ldots \\\hline9x & 145,00\ldots \end{array}\Leftrightarrow x = \dfrac{145}{9}\)
3. \(8,6=\dfrac{86}{10}=\dfrac{43}{5}\)
4. \(x = 10,2\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1028{,}88\ldots \\10x & 102{,}88\ldots \\\hline90x & 926,00\ldots \end{array}\Leftrightarrow x = \dfrac{926}{90}= \dfrac{463}{45}\)
5. \(-10,3=\dfrac{-103}{10}\)
6. \(x = 3,6\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 364{,}44\ldots \\10x & 36{,}44\ldots \\\hline90x & 328,00\ldots \end{array}\Leftrightarrow x = \dfrac{328}{90}= \dfrac{164}{45}\)
7. \(x = 7,673\textbf{717}\textbf{717}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 7673717{,}717717\ldots \\1000x & 7673{,}717717\ldots \\\hline999000x & 7666044,000000\ldots \end{array}\Leftrightarrow x = \dfrac{7666044}{999000}= \dfrac{638837}{83250}\)
8. \(15,32=\dfrac{1532}{100}=\dfrac{383}{25}\)
9. \(x = 20,\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 209{,}99\ldots \\1x & 20{,}99\ldots \\\hline9x & 189,00\ldots \end{array}\Leftrightarrow x = \dfrac{189}{9}= \dfrac{21}{1}\)
10. \(x = 7,\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 77{,}77\ldots \\1x & 7{,}77\ldots \\\hline9x & 70,00\ldots \end{array}\Leftrightarrow x = \dfrac{70}{9}\)
11. \(-3,896=\dfrac{-3896}{1000}=\dfrac{-487}{125}\)
12. \(-11,775=\dfrac{-11775}{1000}=\dfrac{-471}{40}\)