Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(19,3\)
2. \(4,894894\ldots\)
3. \(7,149292\ldots\)
4. \(3,777\ldots\)
5. \(11,74343\ldots\)
6. \(12,36\)
7. \(12,788\ldots\)
8. \(-14,297\)
9. \(-12,93\)
10. \(16,674674\ldots\)
11. \(7,32626\ldots\)
12. \(-2,610\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(19,3=\dfrac{193}{10}\)
2. \(x = 4,\textbf{894}\textbf{894}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 4894,894894\ldots \\1x & 4,894894\ldots \\\hline999x & 4890,000000\ldots \end{array}\Leftrightarrow x = \dfrac{4890}{999}= \dfrac{1630}{333}\)
3. \(x = 7,14\textbf{92}\textbf{92}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 71492,9292\ldots \\100x & 714,9292\ldots \\\hline9900x & 70778,0000\ldots \end{array}\Leftrightarrow x = \dfrac{70778}{9900}= \dfrac{35389}{4950}\)
4. \(x = 3,7\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 377,77\ldots \\10x & 37,77\ldots \\\hline90x & 340,00\ldots \end{array}\Leftrightarrow x = \dfrac{340}{90}= \dfrac{34}{9}\)
5. \(x = 11,7\textbf{43}\textbf{43}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 11743,4343\ldots \\10x & 117,4343\ldots \\\hline990x & 11626,0000\ldots \end{array}\Leftrightarrow x = \dfrac{11626}{990}= \dfrac{5813}{495}\)
6. \(12,36=\dfrac{1236}{100}=\dfrac{309}{25}\)
7. \(x = 12,7\textbf{8}\textbf{8}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1278,88\ldots \\10x & 127,88\ldots \\\hline90x & 1151,00\ldots \end{array}\Leftrightarrow x = \dfrac{1151}{90}\)
8. \(-14,297=\dfrac{-14297}{1000}\)
9. \(-12,93=\dfrac{-1293}{100}\)
10. \(x = 16,\textbf{674}\textbf{674}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 16674,674674\ldots \\1x & 16,674674\ldots \\\hline999x & 16658,000000\ldots \end{array}\Leftrightarrow x = \dfrac{16658}{999}\)
11. \(x = 7,3\textbf{26}\textbf{26}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 7326,2626\ldots \\10x & 73,2626\ldots \\\hline990x & 7253,0000\ldots \end{array}\Leftrightarrow x = \dfrac{7253}{990}\)
12. \(-2,610=\dfrac{-2610}{1000}=\dfrac{-261}{100}\)