# Decimaal naar breuk

#### Zet het decimaal getal om naar een breuk

1. $$17,77601601\ldots$$
2. $$8,791$$
3. $$18,555\ldots$$
4. $$12,178181\ldots$$
5. $$-11,520$$
6. $$4,215689689\ldots$$
7. $$12,96878878\ldots$$
8. $$20,711526526\ldots$$
9. $$0,4164242\ldots$$
10. $$17,347$$
11. $$11,188484\ldots$$
12. $$-3,4$$

#### Zet het decimaal getal om naar een breuk

##### Verbetersleutel

1. $$x = 17,77\textbf{601}\textbf{601}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1777601,601601\ldots \\100x & 1777,601601\ldots \\\hline99900x & 1775824,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1775824}{99900}= \dfrac{443956}{24975}$$
2. $$8,791=\dfrac{8791}{1000}$$
3. $$x = 18,5\textbf{5}\textbf{5}\ldots\Leftrightarrow \begin{array}{ r | r }100x & 1855,55\ldots \\10x & 185,55\ldots \\\hline90x & 1670,00\ldots \end{array}\Leftrightarrow x = \dfrac{1670}{90}= \dfrac{167}{9}$$
4. $$x = 12,17\textbf{81}\textbf{81}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 121781,8181\ldots \\100x & 1217,8181\ldots \\\hline9900x & 120564,0000\ldots \end{array}\Leftrightarrow x = \dfrac{120564}{9900}= \dfrac{3349}{275}$$
5. $$-11,520=\dfrac{-11520}{1000}=\dfrac{-288}{25}$$
6. $$x = 4,215\textbf{689}\textbf{689}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 4215689,689689\ldots \\1000x & 4215,689689\ldots \\\hline999000x & 4211474,000000\ldots \end{array}\Leftrightarrow x = \dfrac{4211474}{999000}= \dfrac{2105737}{499500}$$
7. $$x = 12,96\textbf{878}\textbf{878}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 1296878,878878\ldots \\100x & 1296,878878\ldots \\\hline99900x & 1295582,000000\ldots \end{array}\Leftrightarrow x = \dfrac{1295582}{99900}= \dfrac{647791}{49950}$$
8. $$x = 20,711\textbf{526}\textbf{526}\ldots\Leftrightarrow \begin{array}{ r | r }1000000x & 20711526,526526\ldots \\1000x & 20711,526526\ldots \\\hline999000x & 20690815,000000\ldots \end{array}\Leftrightarrow x = \dfrac{20690815}{999000}= \dfrac{4138163}{199800}$$
9. $$x = 0,416\textbf{42}\textbf{42}\ldots\Leftrightarrow \begin{array}{ r | r }100000x & 41642,4242\ldots \\1000x & 416,4242\ldots \\\hline99000x & 41226,0000\ldots \end{array}\Leftrightarrow x = \dfrac{41226}{99000}= \dfrac{6871}{16500}$$
10. $$17,347=\dfrac{17347}{1000}$$
11. $$x = 11,18\textbf{84}\textbf{84}\ldots\Leftrightarrow \begin{array}{ r | r }10000x & 111884,8484\ldots \\100x & 1118,8484\ldots \\\hline9900x & 110766,0000\ldots \end{array}\Leftrightarrow x = \dfrac{110766}{9900}= \dfrac{18461}{1650}$$
12. $$-3,4=\dfrac{-34}{10}=\dfrac{-17}{5}$$
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 02:24:52