Dezimalentwicklung/2,07 203/Bruch/Aufgabe/Lösung

Es ist

{}{\begin{aligned}2{,}07{\overline {203}}&=2{,}07+0{,}00{\overline {203}}\\&={\frac {207}{100}}+{\frac {1}{100}}\cdot 0{,}{\overline {203}}\\&={\frac {207}{100}}+{\frac {1}{100}}\cdot 203\cdot 0{,}{\overline {001}}\\&={\frac {207}{100}}+{\frac {1}{100}}\cdot 203\cdot {\frac {1}{999}}\\&={\frac {207}{100}}+{\frac {203}{99900}}\\&={\frac {206793+203}{99900}}\\&={\frac {206996}{99900}}\\&={\frac {51749}{24975}}.\end{aligned}}

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