Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(8,36176176\ldots\)
2. \(1,16940940\ldots\)
3. \(2,597\)
4. \(-7,3\)
5. \(3,11\ldots\)
6. \(3,597\)
7. \(5,6366\ldots\)
8. \(11,18377\ldots\)
9. \(4,415\)
10. \(-19,980\)
11. \(13,44\)
12. \(20,36644\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 8,36\textbf{176}\textbf{176}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 836176,176176\ldots \\100x & 836,176176\ldots \\\hline99900x & 835340,000000\ldots \end{array}\Leftrightarrow x = \dfrac{835340}{99900}= \dfrac{41767}{4995}\)
2. \(x = 1,16\textbf{940}\textbf{940}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 116940,94940\ldots \\100x & 116,94094\ldots \\\hline99900x & 116824,000000\ldots \end{array}\Leftrightarrow x = \dfrac{116824}{99900}= \dfrac{29206}{24975}\)
3. \(2,597=\dfrac{2597}{1000}\)
4. \(-7,3=\dfrac{-73}{10}\)
5. \(x = 3,\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 31,11\ldots \\1x & 3,11\ldots \\\hline9x & 28,00\ldots \end{array}\Leftrightarrow x = \dfrac{28}{9}\)
6. \(3,597=\dfrac{3597}{1000}\)
7. \(x = 5,63\textbf{6}\textbf{6}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 5636,66\ldots \\100x & 563,66\ldots \\\hline900x & 5073,00\ldots \end{array}\Leftrightarrow x = \dfrac{5073}{900}= \dfrac{1691}{300}\)
8. \(x = 11,183\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 111837,77\ldots \\1000x & 11183,77\ldots \\\hline9000x & 100654,00\ldots \end{array}\Leftrightarrow x = \dfrac{100654}{9000}= \dfrac{50327}{4500}\)
9. \(4,415=\dfrac{4415}{1000}=\dfrac{883}{200}\)
10. \(-19,980=\dfrac{-19980}{1000}=\dfrac{-999}{50}\)
11. \(13,44=\dfrac{1344}{100}=\dfrac{336}{25}\)
12. \(x = 20,366\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 203664,44\ldots \\1000x & 20366,44\ldots \\\hline9000x & 183298,00\ldots \end{array}\Leftrightarrow x = \dfrac{183298}{9000}= \dfrac{91649}{4500}\)