Decimaal naar breuk

Zet het decimaal getal om naar een breuk

1. $$-3,2$$
2. $$13,9595\ldots$$
3. $$8,90999\ldots$$
4. $$2,4$$
5. $$20,933\ldots$$
6. $$11,27$$
7. $$3,399393\ldots$$
8. $$-12,3$$
9. $$3,211\ldots$$
10. $$4,863232\ldots$$
11. $$0,983983\ldots$$
12. $$2,79786786\ldots$$

Zet het decimaal getal om naar een breuk

Verbetersleutel

1. $$-3,2=\dfrac{-32}{10}=\dfrac{-16}{5}$$
2. $$x = 13,\textbf{95}\textbf{95}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1395,9595\ldots \\1x & 13,9595\ldots \\\hline99x & 1382,0000\ldots \end{array}\Leftrightarrow x = \dfrac{1382}{99}$$
3. $$x = 8,909\textbf{9}\textbf{9}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 89099,99\ldots \\1000x & 8909,99\ldots \\\hline9000x & 80190,00\ldots \end{array}\Leftrightarrow x = \dfrac{80190}{9000}= \dfrac{891}{100}$$
4. $$2,4=\dfrac{24}{10}=\dfrac{12}{5}$$
5. $$x = 20,9\textbf{3}\textbf{3}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 2093,33\ldots \\10x & 209,33\ldots \\\hline90x & 1884,00\ldots \end{array}\Leftrightarrow x = \dfrac{1884}{90}= \dfrac{314}{15}$$
6. $$11,27=\dfrac{1127}{100}$$
7. $$x = 3,39\textbf{93}\textbf{93}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 33993,9393\ldots \\100x & 339,9393\ldots \\\hline9900x & 33654,0000\ldots \end{array}\Leftrightarrow x = \dfrac{33654}{9900}= \dfrac{5609}{1650}$$
8. $$-12,3=\dfrac{-123}{10}$$
9. $$x = 3,2\textbf{1}\textbf{1}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 321,11\ldots \\10x & 32,11\ldots \\\hline90x & 289,00\ldots \end{array}\Leftrightarrow x = \dfrac{289}{90}$$
10. $$x = 4,86\textbf{32}\textbf{32}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 48632,3232\ldots \\100x & 486,3232\ldots \\\hline9900x & 48146,0000\ldots \end{array}\Leftrightarrow x = \dfrac{48146}{9900}= \dfrac{24073}{4950}$$
11. $$x = 0,\textbf{983}\textbf{983}\ldots\Leftrightarrow \begin{array}{ r | r }1000x & 983,983983\ldots \\1x & 0,983983\ldots \\\hline999x & 983,000000\ldots \end{array}\Leftrightarrow x = \dfrac{983}{999}$$
12. $$x = 2,79\textbf{786}\textbf{786}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 279786,786786\ldots \\100x & 279,786786\ldots \\\hline99900x & 279507,000000\ldots \end{array}\Leftrightarrow x = \dfrac{279507}{99900}= \dfrac{93169}{33300}$$
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 08:19:59