Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(19,7977\ldots\)
2. \(1,944\ldots\)
3. \(7,55899\ldots\)
4. \(-16,11\)
5. \(-13,795\)
6. \(15,38\)
7. \(0,56565\ldots\)
8. \(13,8537537\ldots\)
9. \(-4,2\)
10. \(5,49\)
11. \(19,869898\ldots\)
12. \(2,352\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 19,79\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 19797{,}77\ldots \\100x & 1979{,}77\ldots \\\hline900x & 17818,00\ldots \end{array}\Leftrightarrow x = \dfrac{17818}{900}= \dfrac{8909}{450}\)
2. \(x = 1,9\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 194{,}44\ldots \\10x & 19{,}44\ldots \\\hline90x & 175,00\ldots \end{array}\Leftrightarrow x = \dfrac{175}{90}= \dfrac{35}{18}\)
3. \(x = 7,558\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 75589{,}99\ldots \\1000x & 7558{,}99\ldots \\\hline9000x & 68031,00\ldots \end{array}\Leftrightarrow x = \dfrac{68031}{9000}= \dfrac{7559}{1000}\)
4. \(-16,11=\dfrac{-1611}{100}\)
5. \(-13,795=\dfrac{-13795}{1000}=\dfrac{-2759}{200}\)
6. \(15,38=\dfrac{1538}{100}=\dfrac{769}{50}\)
7. \(x = 0,5\textbf{65}\textbf{65}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 565{,}6565\ldots \\10x & 5{,}6565\ldots \\\hline990x & 560,0000\ldots \end{array}\Leftrightarrow x = \dfrac{560}{990}= \dfrac{56}{99}\)
8. \(x = 13,8\textbf{537}\textbf{537}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 138537{,}537537\ldots \\10x & 138{,}537537\ldots \\\hline9990x & 138399,000000\ldots \end{array}\Leftrightarrow x = \dfrac{138399}{9990}= \dfrac{46133}{3330}\)
9. \(-4,2=\dfrac{-42}{10}=\dfrac{-21}{5}\)
10. \(5,49=\dfrac{549}{100}\)
11. \(x = 19,86\textbf{98}\textbf{98}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 198698{,}9898\ldots \\100x & 1986{,}9898\ldots \\\hline9900x & 196712,0000\ldots \end{array}\Leftrightarrow x = \dfrac{196712}{9900}= \dfrac{49178}{2475}\)
12. \(2,352=\dfrac{2352}{1000}=\dfrac{294}{125}\)