Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(3,9935454\ldots\)
2. \(16,907341341\ldots\)
3. \(11,1655\ldots\)
4. \(15,310\)
5. \(1,5\)
6. \(10,232918918\ldots\)
7. \(-20,6\)
8. \(12,33\ldots\)
9. \(3,3\)
10. \(6,66\ldots\)
11. \(17,426868\ldots\)
12. \(15,26\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 3,993\textbf{54}\textbf{54}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 399354{,}5454\ldots \\1000x & 3993{,}5454\ldots \\\hline99000x & 395361,0000\ldots \end{array}\Leftrightarrow x = \dfrac{395361}{99000}= \dfrac{43929}{11000}\)
2. \(x = 16,907\textbf{341}\textbf{341}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 16907341{,}341341\ldots \\1000x & 16907{,}341341\ldots \\\hline999000x & 16890434,000000\ldots \end{array}\Leftrightarrow x = \dfrac{16890434}{999000}= \dfrac{8445217}{499500}\)
3. \(x = 11,16\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 11165{,}55\ldots \\100x & 1116{,}55\ldots \\\hline900x & 10049,00\ldots \end{array}\Leftrightarrow x = \dfrac{10049}{900}\)
4. \(15,310=\dfrac{15310}{1000}=\dfrac{1531}{100}\)
5. \(1,5=\dfrac{15}{10}=\dfrac{3}{2}\)
6. \(x = 10,232\textbf{918}\textbf{918}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 10232918{,}918918\ldots \\1000x & 10232{,}918918\ldots \\\hline999000x & 10222686,000000\ldots \end{array}\Leftrightarrow x = \dfrac{10222686}{999000}= \dfrac{189309}{18500}\)
7. \(-20,6=\dfrac{-206}{10}=\dfrac{-103}{5}\)
8. \(x = 12,\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 123{,}33\ldots \\1x & 12{,}33\ldots \\\hline9x & 111,00\ldots \end{array}\Leftrightarrow x = \dfrac{111}{9}= \dfrac{37}{3}\)
9. \(3,3=\dfrac{33}{10}\)
10. \(x = 6,\textbf{6}\textbf{6}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 66{,}66\ldots \\1x & 6{,}66\ldots \\\hline9x & 60,00\ldots \end{array}\Leftrightarrow x = \dfrac{60}{9}= \dfrac{20}{3}\)
11. \(x = 17,42\textbf{68}\textbf{68}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 174268{,}6868\ldots \\100x & 1742{,}6868\ldots \\\hline9900x & 172526,0000\ldots \end{array}\Leftrightarrow x = \dfrac{172526}{9900}= \dfrac{86263}{4950}\)
12. \(15,26=\dfrac{1526}{100}=\dfrac{763}{50}\)