Math Problem Solver

\[\frac{1.20 \cdot {10}^{21}}{6.02} \cdot {10}^{23} = \frac{6000000000000000000000000000000000000000000000}{301} = 19933554817275747508305647840531561461794019.\overline{933554817275747508305647840531561461794019}\]

\[\begin{aligned}\frac{1.20 \cdot {10}^{21}}{6.02} \cdot {10}^{23}& = \left(1 + \frac{2}{10}\right) \cdot 10^{21} \cdot \frac{1}{6 + \frac{2}{100}} \cdot 10^{23}\\& = \left(1 + \frac{1}{5}\right) \cdot 10^{21} \cdot \frac{1}{6 + \frac{2}{100}} \cdot 10^{23}\\& = \frac{6}{5} \cdot 10^{21} \cdot \frac{1}{6 + \frac{2}{100}} \cdot 10^{23}\\& = \frac{6}{5} \cdot 1000000000000000000000 \cdot \frac{1}{6 + \frac{2}{100}} \cdot 10^{23}\\& = \frac{6}{5} \cdot 1000000000000000000000 \cdot \frac{1}{6 + \frac{1}{50}} \cdot 10^{23}\\& = \frac{6}{5} \cdot 1000000000000000000000 \cdot \frac{1}{\frac{301}{50}} \cdot 10^{23}\\& = \frac{6}{5} \cdot 1000000000000000000000 \cdot \frac{50}{301} \cdot 10^{23}\\& = \frac{6}{5} \cdot 1000000000000000000000 \cdot \frac{50}{301} \cdot 100000000000000000000000\\& = 1200000000000000000000 \cdot \frac{50}{301} \cdot 100000000000000000000000\\& = \frac{60000000000000000000000}{301} \cdot 100000000000000000000000\\& = \frac{6000000000000000000000000000000000000000000000}{301}\end{aligned}\]