Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(2,177764764\ldots\)
2. \(5,6\)
3. \(7,5342929\ldots\)
4. \(3,611852852\ldots\)
5. \(1,644\ldots\)
6. \(3,498\)
7. \(13,899595\ldots\)
8. \(3,82988\ldots\)
9. \(-19,245\)
10. \(-6,11\)
11. \(8,100\)
12. \(5,65\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 2,177\textbf{764}\textbf{764}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 2177764{,}764764\ldots \\1000x & 2177{,}764764\ldots \\\hline999000x & 2175587,000000\ldots \end{array}\Leftrightarrow x = \dfrac{2175587}{999000}\)
2. \(5,6=\dfrac{56}{10}=\dfrac{28}{5}\)
3. \(x = 7,534\textbf{29}\textbf{29}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 753429{,}2929\ldots \\1000x & 7534{,}2929\ldots \\\hline99000x & 745895,0000\ldots \end{array}\Leftrightarrow x = \dfrac{745895}{99000}= \dfrac{149179}{19800}\)
4. \(x = 3,611\textbf{852}\textbf{852}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 3611852{,}852852\ldots \\1000x & 3611{,}852852\ldots \\\hline999000x & 3608241,000000\ldots \end{array}\Leftrightarrow x = \dfrac{3608241}{999000}= \dfrac{1202747}{333000}\)
5. \(x = 1,6\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 164{,}44\ldots \\10x & 16{,}44\ldots \\\hline90x & 148,00\ldots \end{array}\Leftrightarrow x = \dfrac{148}{90}= \dfrac{74}{45}\)
6. \(3,498=\dfrac{3498}{1000}=\dfrac{1749}{500}\)
7. \(x = 13,89\textbf{95}\textbf{95}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 138995{,}9595\ldots \\100x & 1389{,}9595\ldots \\\hline9900x & 137606,0000\ldots \end{array}\Leftrightarrow x = \dfrac{137606}{9900}= \dfrac{68803}{4950}\)
8. \(x = 3,829\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 38298{,}88\ldots \\1000x & 3829{,}88\ldots \\\hline9000x & 34469,00\ldots \end{array}\Leftrightarrow x = \dfrac{34469}{9000}\)
9. \(-19,245=\dfrac{-19245}{1000}=\dfrac{-3849}{200}\)
10. \(-6,11=\dfrac{-611}{100}\)
11. \(8,100=\dfrac{8100}{1000}=\dfrac{81}{10}\)
12. \(5,65=\dfrac{565}{100}=\dfrac{113}{20}\)