Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(1,6434141\ldots\)
2. \(15,8871871\ldots\)
3. \(-17,55\)
4. \(6,426108108\ldots\)
5. \(-13,971\)
6. \(13,8918918\ldots\)
7. \(-18,8\)
8. \(10,59\)
9. \(4,8106106\ldots\)
10. \(13,87792792\ldots\)
11. \(15,4785785\ldots\)
12. \(4,81808808\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 1,643\textbf{41}\textbf{41}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 164341{,}4141\ldots \\1000x & 1643{,}4141\ldots \\\hline99000x & 162698,0000\ldots \end{array}\Leftrightarrow x = \dfrac{162698}{99000}= \dfrac{81349}{49500}\)
2. \(x = 15,8\textbf{871}\textbf{871}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 158871{,}871871\ldots \\10x & 158{,}871871\ldots \\\hline9990x & 158713,000000\ldots \end{array}\Leftrightarrow x = \dfrac{158713}{9990}\)
3. \(-17,55=\dfrac{-1755}{100}=\dfrac{-351}{20}\)
4. \(x = 6,426\textbf{108}\textbf{108}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 6426108{,}108108\ldots \\1000x & 6426{,}108108\ldots \\\hline999000x & 6419682,000000\ldots \end{array}\Leftrightarrow x = \dfrac{6419682}{999000}= \dfrac{118883}{18500}\)
5. \(-13,971=\dfrac{-13971}{1000}\)
6. \(x = 13,8\textbf{918}\textbf{918}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 138918{,}918918\ldots \\10x & 138{,}918918\ldots \\\hline9990x & 138780,000000\ldots \end{array}\Leftrightarrow x = \dfrac{138780}{9990}= \dfrac{514}{37}\)
7. \(-18,8=\dfrac{-188}{10}=\dfrac{-94}{5}\)
8. \(10,59=\dfrac{1059}{100}\)
9. \(x = 4,8\textbf{106}\textbf{106}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 48106{,}106106\ldots \\10x & 48{,}106106\ldots \\\hline9990x & 48058,000000\ldots \end{array}\Leftrightarrow x = \dfrac{48058}{9990}= \dfrac{24029}{4995}\)
10. \(x = 13,87\textbf{792}\textbf{792}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1387792{,}792792\ldots \\100x & 1387{,}792792\ldots \\\hline99900x & 1386405,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1386405}{99900}= \dfrac{30809}{2220}\)
11. \(x = 15,4\textbf{785}\textbf{785}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 154785{,}785785\ldots \\10x & 154{,}785785\ldots \\\hline9990x & 154631,000000\ldots \end{array}\Leftrightarrow x = \dfrac{154631}{9990}\)
12. \(x = 4,81\textbf{808}\textbf{808}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 481808{,}808808\ldots \\100x & 481{,}808808\ldots \\\hline99900x & 481327,000000\ldots \end{array}\Leftrightarrow x = \dfrac{481327}{99900}\)