Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(1,714714\ldots\)
2. \(8,33\ldots\)
3. \(3,482\)
4. \(16,79394394\ldots\)
5. \(6,44377\ldots\)
6. \(-9,340\)
7. \(18,3\)
8. \(9,4949\ldots\)
9. \(6,4646\ldots\)
10. \(11,4117070\ldots\)
11. \(11,535\)
12. \(15,4949\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 1,\textbf{714}\textbf{714}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 1714{,}714714\ldots \\1x & 1{,}714714\ldots \\\hline999x & 1713,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1713}{999}= \dfrac{571}{333}\)
2. \(x = 8,\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 83{,}33\ldots \\1x & 8{,}33\ldots \\\hline9x & 75,00\ldots \end{array}\Leftrightarrow x = \dfrac{75}{9}= \dfrac{25}{3}\)
3. \(3,482=\dfrac{3482}{1000}=\dfrac{1741}{500}\)
4. \(x = 16,79\textbf{394}\textbf{394}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1679394{,}394394\ldots \\100x & 1679{,}394394\ldots \\\hline99900x & 1677715,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1677715}{99900}= \dfrac{335543}{19980}\)
5. \(x = 6,443\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 64437{,}77\ldots \\1000x & 6443{,}77\ldots \\\hline9000x & 57994,00\ldots \end{array}\Leftrightarrow x = \dfrac{57994}{9000}= \dfrac{28997}{4500}\)
6. \(-9,340=\dfrac{-9340}{1000}=\dfrac{-467}{50}\)
7. \(18,3=\dfrac{183}{10}\)
8. \(x = 9,\textbf{49}\textbf{49}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 949{,}4949\ldots \\1x & 9{,}4949\ldots \\\hline99x & 940,0000\ldots \end{array}\Leftrightarrow x = \dfrac{940}{99}\)
9. \(x = 6,\textbf{46}\textbf{46}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 646{,}4646\ldots \\1x & 6{,}4646\ldots \\\hline99x & 640,0000\ldots \end{array}\Leftrightarrow x = \dfrac{640}{99}\)
10. \(x = 11,411\textbf{70}\textbf{70}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1141170{,}770\ldots \\1000x & 11411{,}707\ldots \\\hline99000x & 1129759,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1129759}{99000}\)
11. \(11,535=\dfrac{11535}{1000}=\dfrac{2307}{200}\)
12. \(x = 15,\textbf{49}\textbf{49}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1549{,}4949\ldots \\1x & 15{,}4949\ldots \\\hline99x & 1534,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1534}{99}\)