Math Problem Solver

\[\frac{6.673 \cdot 10 - 11 \cdot 5.98 \cdot 1024 \cdot 1.99 \cdot 1030}{160 \cdot 109} = - \frac{69032550827}{8720000} = -7916.5769297\overline{018348623853211009174311926605504587155963302752293577981651376146788990825688073394495412844036697247706422}\]

\[\begin{aligned}\frac{6.673 \cdot 10 - 11 \cdot 5.98 \cdot 1024 \cdot 1.99 \cdot 1030}{160 \cdot 109}& = \left(\left(6 + \frac{673}{1000}\right) \cdot 10 - 11 \cdot \left(5 + \frac{98}{100}\right) \cdot 1024 \cdot \left(1 + \frac{99}{100}\right) \cdot 1030\right) \cdot \frac{1}{160 \cdot 109}\\& = \left(\frac{6673}{1000} \cdot 10 - 11 \cdot \left(5 + \frac{98}{100}\right) \cdot 1024 \cdot \left(1 + \frac{99}{100}\right) \cdot 1030\right) \cdot \frac{1}{160 \cdot 109}\\& = \left(\frac{6673}{100} - 11 \cdot \left(5 + \frac{98}{100}\right) \cdot 1024 \cdot \left(1 + \frac{99}{100}\right) \cdot 1030\right) \cdot \frac{1}{160 \cdot 109}\\& = \left(\frac{6673}{100} - 11 \cdot \left(5 + \frac{49}{50}\right) \cdot 1024 \cdot \left(1 + \frac{99}{100}\right) \cdot 1030\right) \cdot \frac{1}{160 \cdot 109}\\& = \left(\frac{6673}{100} - 11 \cdot \frac{299}{50} \cdot 1024 \cdot \left(1 + \frac{99}{100}\right) \cdot 1030\right) \cdot \frac{1}{160 \cdot 109}\\& = \left(\frac{6673}{100} - 11 \cdot \frac{299}{50} \cdot 1024 \cdot \frac{199}{100} \cdot 1030\right) \cdot \frac{1}{160 \cdot 109}\\& = \left(\frac{6673}{100} - \frac{3289}{50} \cdot 1024 \cdot \frac{199}{100} \cdot 1030\right) \cdot \frac{1}{160 \cdot 109}\\& = \left(\frac{6673}{100} - \frac{1683968}{25} \cdot \frac{199}{100} \cdot 1030\right) \cdot \frac{1}{160 \cdot 109}\\& = \left(\frac{6673}{100} - \frac{83777408}{625} \cdot 1030\right) \cdot \frac{1}{160 \cdot 109}\\& = \left(\frac{6673}{100} - \frac{17258146048}{125}\right) \cdot \frac{1}{160 \cdot 109}\\& = - \frac{69032550827}{500} \cdot \frac{1}{160 \cdot 109}\\& = - \frac{69032550827}{500} \cdot \frac{1}{17440}\\& = - \frac{69032550827}{8720000}\end{aligned}\]