Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(7,49170170\ldots\)
2. \(1,1316767\ldots\)
3. \(-18,518\)
4. \(15,734141\ldots\)
5. \(17,86\)
6. \(-15,986\)
7. \(0,33\ldots\)
8. \(0,877\ldots\)
9. \(17,357\)
10. \(-18,2\)
11. \(-14,9\)
12. \(-12,5\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 7,49\textbf{170}\textbf{170}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 749170{,}17170\ldots \\100x & 749{,}17017\ldots \\\hline99900x & 748421,000000\ldots \end{array}\Leftrightarrow x = \dfrac{748421}{99900}\)
2. \(x = 1,131\textbf{67}\textbf{67}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 113167{,}6767\ldots \\1000x & 1131{,}6767\ldots \\\hline99000x & 112036,0000\ldots \end{array}\Leftrightarrow x = \dfrac{112036}{99000}= \dfrac{28009}{24750}\)
3. \(-18,518=\dfrac{-18518}{1000}=\dfrac{-9259}{500}\)
4. \(x = 15,73\textbf{41}\textbf{41}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 157341{,}4141\ldots \\100x & 1573{,}4141\ldots \\\hline9900x & 155768,0000\ldots \end{array}\Leftrightarrow x = \dfrac{155768}{9900}= \dfrac{38942}{2475}\)
5. \(17,86=\dfrac{1786}{100}=\dfrac{893}{50}\)
6. \(-15,986=\dfrac{-15986}{1000}=\dfrac{-7993}{500}\)
7. \(x = 0,\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 3{,}33\ldots \\1x & 0{,}33\ldots \\\hline9x & 3,00\ldots \end{array}\Leftrightarrow x = \dfrac{3}{9}= \dfrac{1}{3}\)
8. \(x = 0,8\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 87{,}77\ldots \\10x & 8{,}77\ldots \\\hline90x & 79,00\ldots \end{array}\Leftrightarrow x = \dfrac{79}{90}\)
9. \(17,357=\dfrac{17357}{1000}\)
10. \(-18,2=\dfrac{-182}{10}=\dfrac{-91}{5}\)
11. \(-14,9=\dfrac{-149}{10}\)
12. \(-12,5=\dfrac{-125}{10}=\dfrac{-25}{2}\)