Decimaal naar breuk

Hoofdmenu Eentje per keer  🖨

Zet het decimaal getal om naar een breuk

1. \(18,8\)
2. \(12,48366\ldots\)
3. \(11,65959\ldots\)
4. \(0,89655\ldots\)
5. \(-3,328\)
6. \(5,6\)
7. \(16,20931931\ldots\)
8. \(3,6\)
9. \(1,5399\ldots\)
10. \(7,2\)
11. \(19,84242\ldots\)
12. \(14,44\ldots\)

---

Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(18,8=\dfrac{188}{10}=\dfrac{94}{5}\)
2. \(x = 12,483\textbf{6}\textbf{6}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 124836{,}66\ldots \\1000x & 12483{,}66\ldots \\\hline9000x & 112353,00\ldots \end{array}\Leftrightarrow x = \dfrac{112353}{9000}= \dfrac{37451}{3000}\)
3. \(x = 11,6\textbf{59}\textbf{59}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 11659{,}5959\ldots \\10x & 116{,}5959\ldots \\\hline990x & 11543,0000\ldots \end{array}\Leftrightarrow x = \dfrac{11543}{990}\)
4. \(x = 0,896\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 8965{,}55\ldots \\1000x & 896{,}55\ldots \\\hline9000x & 8069,00\ldots \end{array}\Leftrightarrow x = \dfrac{8069}{9000}\)
5. \(-3,328=\dfrac{-3328}{1000}=\dfrac{-416}{125}\)
6. \(5,6=\dfrac{56}{10}=\dfrac{28}{5}\)
7. \(x = 16,20\textbf{931}\textbf{931}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1620931{,}931931\ldots \\100x & 1620{,}931931\ldots \\\hline99900x & 1619311,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1619311}{99900}\)
8. \(3,6=\dfrac{36}{10}=\dfrac{18}{5}\)
9. \(x = 1,53\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 1539{,}99\ldots \\100x & 153{,}99\ldots \\\hline900x & 1386,00\ldots \end{array}\Leftrightarrow x = \dfrac{1386}{900}= \dfrac{77}{50}\)
10. \(7,2=\dfrac{72}{10}=\dfrac{36}{5}\)
11. \(x = 19,8\textbf{42}\textbf{42}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 19842{,}4242\ldots \\10x & 198{,}4242\ldots \\\hline990x & 19644,0000\ldots \end{array}\Leftrightarrow x = \dfrac{19644}{990}= \dfrac{3274}{165}\)
12. \(x = 14,\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 144{,}44\ldots \\1x & 14{,}44\ldots \\\hline9x & 130,00\ldots \end{array}\Leftrightarrow x = \dfrac{130}{9}\)