Decimaal naar breuk

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Zet het decimaal getal om naar een breuk

1. \(-3,43\)
2. \(-18,68\)
3. \(1,5\)
4. \(7,546546\ldots\)
5. \(12,22\ldots\)
6. \(9,3570570\ldots\)
7. \(10,9222\ldots\)
8. \(13,293\)
9. \(-18,89\)
10. \(-16,9\)
11. \(0,44\ldots\)
12. \(17,15111\ldots\)

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Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(-3,43=\dfrac{-343}{100}\)
2. \(-18,68=\dfrac{-1868}{100}=\dfrac{-467}{25}\)
3. \(1,5=\dfrac{15}{10}=\dfrac{3}{2}\)
4. \(x = 7,\textbf{546}\textbf{546}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 7546{,}546546\ldots \\1x & 7{,}546546\ldots \\\hline999x & 7539,000000\ldots \end{array}\Leftrightarrow x = \dfrac{7539}{999}= \dfrac{2513}{333}\)
5. \(x = 12,\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 122{,}22\ldots \\1x & 12{,}22\ldots \\\hline9x & 110,00\ldots \end{array}\Leftrightarrow x = \dfrac{110}{9}\)
6. \(x = 9,3\textbf{570}\textbf{570}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 93570{,}57570\ldots \\10x & 93{,}57057\ldots \\\hline9990x & 93477,000000\ldots \end{array}\Leftrightarrow x = \dfrac{93477}{9990}= \dfrac{31159}{3330}\)
7. \(x = 10,92\textbf{2}\textbf{2}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 10922{,}22\ldots \\100x & 1092{,}22\ldots \\\hline900x & 9830,00\ldots \end{array}\Leftrightarrow x = \dfrac{9830}{900}= \dfrac{983}{90}\)
8. \(13,293=\dfrac{13293}{1000}\)
9. \(-18,89=\dfrac{-1889}{100}\)
10. \(-16,9=\dfrac{-169}{10}\)
11. \(x = 0,\textbf{4}\textbf{4}\ldots\Leftrightarrow \begin{array}{ r | r }10x & 4{,}44\ldots \\1x & 0{,}44\ldots \\\hline9x & 4,00\ldots \end{array}\Leftrightarrow x = \dfrac{4}{9}\)
12. \(x = 17,151\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 171511{,}11\ldots \\1000x & 17151{,}11\ldots \\\hline9000x & 154360,00\ldots \end{array}\Leftrightarrow x = \dfrac{154360}{9000}= \dfrac{3859}{225}\)