Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(12,372\)
2. \(17,2\)
3. \(6,654907907\ldots\)
4. \(8,99\ldots\)
5. \(8,88352352\ldots\)
6. \(-19,3\)
7. \(-15,786\)
8. \(20,7415050\ldots\)
9. \(8,233\ldots\)
10. \(9,80\)
11. \(-17,35\)
12. \(-12,5\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(12,372=\dfrac{12372}{1000}=\dfrac{3093}{250}\)
2. \(17,2=\dfrac{172}{10}=\dfrac{86}{5}\)
3. \(x = 6,654\textbf{907}\textbf{907}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 6654907{,}907907\ldots \\1000x & 6654{,}907907\ldots \\\hline999000x & 6648253,000000\ldots \end{array}\Leftrightarrow x = \dfrac{6648253}{999000}\)
4. \(x = 8,\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 89{,}99\ldots \\1x & 8{,}99\ldots \\\hline9x & 81,00\ldots \end{array}\Leftrightarrow x = \dfrac{81}{9}= \dfrac{9}{1}\)
5. \(x = 8,88\textbf{352}\textbf{352}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 888352{,}352352\ldots \\100x & 888{,}352352\ldots \\\hline99900x & 887464,000000\ldots \end{array}\Leftrightarrow x = \dfrac{887464}{99900}= \dfrac{221866}{24975}\)
6. \(-19,3=\dfrac{-193}{10}\)
7. \(-15,786=\dfrac{-15786}{1000}=\dfrac{-7893}{500}\)
8. \(x = 20,741\textbf{50}\textbf{50}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 2074150{,}550\ldots \\1000x & 20741{,}505\ldots \\\hline99000x & 2053409,0000\ldots \end{array}\Leftrightarrow x = \dfrac{2053409}{99000}\)
9. \(x = 8,2\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 823{,}33\ldots \\10x & 82{,}33\ldots \\\hline90x & 741,00\ldots \end{array}\Leftrightarrow x = \dfrac{741}{90}= \dfrac{247}{30}\)
10. \(9,80=\dfrac{980}{100}=\dfrac{49}{5}\)
11. \(-17,35=\dfrac{-1735}{100}=\dfrac{-347}{20}\)
12. \(-12,5=\dfrac{-125}{10}=\dfrac{-25}{2}\)