Decimaal naar breuk

Hoofdmenu Eentje per keer  🖨

Zet het decimaal getal om naar een breuk

1. \(11,534534\ldots\)
2. \(13,284716716\ldots\)
3. \(1,866\ldots\)
4. \(-9,41\)
5. \(4,3737\ldots\)
6. \(-20,6\)
7. \(20,5\)
8. \(15,39\)
9. \(19,53101101\ldots\)
10. \(19,6\)
11. \(11,702698698\ldots\)
12. \(16,266\)

---

Zet het decimaal getal om naar een breuk

Verbetersleutel

1. \(x = 11,\textbf{534}\textbf{534}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 11534,534534\ldots \\1x & 11,534534\ldots \\\hline999x & 11523,000000\ldots \end{array}\Leftrightarrow x = \dfrac{11523}{999}= \dfrac{3841}{333}\)
2. \(x = 13,284\textbf{716}\textbf{716}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 13284716,716716\ldots \\1000x & 13284,716716\ldots \\\hline999000x & 13271432,000000\ldots \end{array}\Leftrightarrow x = \dfrac{13271432}{999000}= \dfrac{1658929}{124875}\)
3. \(x = 1,8\textbf{6}\textbf{6}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 186,66\ldots \\10x & 18,66\ldots \\\hline90x & 168,00\ldots \end{array}\Leftrightarrow x = \dfrac{168}{90}= \dfrac{28}{15}\)
4. \(-9,41=\dfrac{-941}{100}\)
5. \(x = 4,\textbf{37}\textbf{37}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 437,3737\ldots \\1x & 4,3737\ldots \\\hline99x & 433,0000\ldots \end{array}\Leftrightarrow x = \dfrac{433}{99}\)
6. \(-20,6=\dfrac{-206}{10}=\dfrac{-103}{5}\)
7. \(20,5=\dfrac{205}{10}=\dfrac{41}{2}\)
8. \(15,39=\dfrac{1539}{100}\)
9. \(x = 19,53\textbf{101}\textbf{101}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1953101,101101\ldots \\100x & 1953,101101\ldots \\\hline99900x & 1951148,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1951148}{99900}= \dfrac{487787}{24975}\)
10. \(19,6=\dfrac{196}{10}=\dfrac{98}{5}\)
11. \(x = 11,702\textbf{698}\textbf{698}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 11702698,698698\ldots \\1000x & 11702,698698\ldots \\\hline999000x & 11690996,000000\ldots \end{array}\Leftrightarrow x = \dfrac{11690996}{999000}= \dfrac{2922749}{249750}\)
12. \(16,266=\dfrac{16266}{1000}=\dfrac{8133}{500}\)