Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(-12,89\)
2. \(-12,304\)
3. \(12,729795795\ldots\)
4. \(5,172\)
5. \(-4,647\)
6. \(12,819\)
7. \(16,435\)
8. \(13,7613131\ldots\)
9. \(6,43744\ldots\)
10. \(-1,4\)
11. \(3,2899\ldots\)
12. \(-3,47\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(-12,89=\dfrac{-1289}{100}\)
2. \(-12,304=\dfrac{-12304}{1000}=\dfrac{-1538}{125}\)
3. \(x = 12,729\textbf{795}\textbf{795}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 12729795{,}795795\ldots \\1000x & 12729{,}795795\ldots \\\hline999000x & 12717066,000000\ldots \end{array}\Leftrightarrow x = \dfrac{12717066}{999000}= \dfrac{2119511}{166500}\)
4. \(5,172=\dfrac{5172}{1000}=\dfrac{1293}{250}\)
5. \(-4,647=\dfrac{-4647}{1000}\)
6. \(12,819=\dfrac{12819}{1000}\)
7. \(16,435=\dfrac{16435}{1000}=\dfrac{3287}{200}\)
8. \(x = 13,761\textbf{31}\textbf{31}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1376131{,}3131\ldots \\1000x & 13761{,}3131\ldots \\\hline99000x & 1362370,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1362370}{99000}= \dfrac{136237}{9900}\)
9. \(x = 6,437\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 64374{,}44\ldots \\1000x & 6437{,}44\ldots \\\hline9000x & 57937,00\ldots \end{array}\Leftrightarrow x = \dfrac{57937}{9000}\)
10. \(-1,4=\dfrac{-14}{10}=\dfrac{-7}{5}\)
11. \(x = 3,28\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 3289{,}99\ldots \\100x & 328{,}99\ldots \\\hline900x & 2961,00\ldots \end{array}\Leftrightarrow x = \dfrac{2961}{900}= \dfrac{329}{100}\)
12. \(-3,47=\dfrac{-347}{100}\)