Dezimalentwicklung/7,103 4002/Bruch/Aufgabe/Lösung

Es ist

${}{\begin{aligned}7{,}103{\overline {4002}}&=7{,}103+0{,}000{\overline {4002}}\\&={\frac {7103}{1000}}+{\frac {1}{1000}}\cdot 0{,}{\overline {4002}}\\&={\frac {7103}{1000}}+{\frac {1}{1000}}\cdot 4002\cdot 0{,}{\overline {0001}}\\&={\frac {7103}{1000}}+{\frac {1}{1000}}\cdot 4002\cdot {\frac {1}{9999}}\\&={\frac {7103\cdot 9999}{9999000}}+{\frac {4002}{9999000}}\\&={\frac {71022897}{9999000}}+{\frac {4002}{9999000}}\\&={\frac {71026899}{9999000}}\\&={\frac {23675633}{3333000}}.\end{aligned}}$

Zur gelösten Aufgabe