Decimaal naar breuk

Hoofdmenu Eentje per keer  🖨

Zet het decimaal getal om naar een breuk

1. \(16,974949\ldots\)
2. \(2,142\)
3. \(10,66\ldots\)
4. \(12,9421421\ldots\)
5. \(19,476476\ldots\)
6. \(3,62844\ldots\)
7. \(4,96150150\ldots\)
8. \(6,36\)
9. \(-1,570\)
10. \(4,839\)
11. \(-19,229\)
12. \(-9,676\)

---

Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 16,97\textbf{49}\textbf{49}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 169749{,}4949\ldots \\100x & 1697{,}4949\ldots \\\hline9900x & 168052,0000\ldots \end{array}\Leftrightarrow x = \dfrac{168052}{9900}= \dfrac{42013}{2475}\)
2. \(2,142=\dfrac{2142}{1000}=\dfrac{1071}{500}\)
3. \(x = 10,\textbf{6}\textbf{6}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 106{,}66\ldots \\1x & 10{,}66\ldots \\\hline9x & 96,00\ldots \end{array}\Leftrightarrow x = \dfrac{96}{9}= \dfrac{32}{3}\)
4. \(x = 12,9\textbf{421}\textbf{421}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 129421{,}421421\ldots \\10x & 129{,}421421\ldots \\\hline9990x & 129292,000000\ldots \end{array}\Leftrightarrow x = \dfrac{129292}{9990}= \dfrac{64646}{4995}\)
5. \(x = 19,\textbf{476}\textbf{476}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 19476{,}476476\ldots \\1x & 19{,}476476\ldots \\\hline999x & 19457,000000\ldots \end{array}\Leftrightarrow x = \dfrac{19457}{999}\)
6. \(x = 3,628\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 36284{,}44\ldots \\1000x & 3628{,}44\ldots \\\hline9000x & 32656,00\ldots \end{array}\Leftrightarrow x = \dfrac{32656}{9000}= \dfrac{4082}{1125}\)
7. \(x = 4,96\textbf{150}\textbf{150}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 496150{,}15150\ldots \\100x & 496{,}15015\ldots \\\hline99900x & 495654,000000\ldots \end{array}\Leftrightarrow x = \dfrac{495654}{99900}= \dfrac{82609}{16650}\)
8. \(6,36=\dfrac{636}{100}=\dfrac{159}{25}\)
9. \(-1,570=\dfrac{-1570}{1000}=\dfrac{-157}{100}\)
10. \(4,839=\dfrac{4839}{1000}\)
11. \(-19,229=\dfrac{-19229}{1000}\)
12. \(-9,676=\dfrac{-9676}{1000}=\dfrac{-2419}{250}\)