Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(2,2\)
2. \(18,879267267\ldots\)
3. \(-11,80\)
4. \(10,5\)
5. \(1,36\)
6. \(1,6\)
7. \(13,9577\ldots\)
8. \(-15,239\)
9. \(18,853853\ldots\)
10. \(0,44\ldots\)
11. \(15,77\ldots\)
12. \(-4,2\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(2,2=\dfrac{22}{10}=\dfrac{11}{5}\)
2. \(x = 18,879\textbf{267}\textbf{267}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 18879267{,}267267\ldots \\1000x & 18879{,}267267\ldots \\\hline999000x & 18860388,000000\ldots \end{array}\Leftrightarrow x = \dfrac{18860388}{999000}= \dfrac{1571699}{83250}\)
3. \(-11,80=\dfrac{-1180}{100}=\dfrac{-59}{5}\)
4. \(10,5=\dfrac{105}{10}=\dfrac{21}{2}\)
5. \(1,36=\dfrac{136}{100}=\dfrac{34}{25}\)
6. \(1,6=\dfrac{16}{10}=\dfrac{8}{5}\)
7. \(x = 13,95\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 13957{,}77\ldots \\100x & 1395{,}77\ldots \\\hline900x & 12562,00\ldots \end{array}\Leftrightarrow x = \dfrac{12562}{900}= \dfrac{6281}{450}\)
8. \(-15,239=\dfrac{-15239}{1000}\)
9. \(x = 18,\textbf{853}\textbf{853}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 18853{,}853853\ldots \\1x & 18{,}853853\ldots \\\hline999x & 18835,000000\ldots \end{array}\Leftrightarrow x = \dfrac{18835}{999}\)
10. \(x = 0,\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 4{,}44\ldots \\1x & 0{,}44\ldots \\\hline9x & 4,00\ldots \end{array}\Leftrightarrow x = \dfrac{4}{9}\)
11. \(x = 15,\textbf{7}\textbf{7}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 157{,}77\ldots \\1x & 15{,}77\ldots \\\hline9x & 142,00\ldots \end{array}\Leftrightarrow x = \dfrac{142}{9}\)
12. \(-4,2=\dfrac{-42}{10}=\dfrac{-21}{5}\)