1.20 x 10^21 / (6.02 x 10^23)

asked by guest
on Nov 14, 2024 at 5:22 pm



You asked:

Evaluate the expression: \(\frac{1.20 \cdot {10}^{21}}{6.02 \cdot {10}^{23}}\)

MathBot Answer:

\[\frac{1.20 \cdot {10}^{21}}{6.02 \cdot {10}^{23}} = \frac{3}{1505} = 0.0\overline{019933554817275747508305647840531561461794}\]

\[\begin{aligned}\frac{1.20 \cdot {10}^{21}}{6.02 \cdot {10}^{23}}& = \left(1 + \frac{2}{10}\right) \cdot 10^{21} \cdot \frac{1}{\left(6 + \frac{2}{100}\right) \cdot 10^{23}}\\& = \left(1 + \frac{1}{5}\right) \cdot 10^{21} \cdot \frac{1}{\left(6 + \frac{2}{100}\right) \cdot 10^{23}}\\& = \frac{6}{5} \cdot 10^{21} \cdot \frac{1}{\left(6 + \frac{2}{100}\right) \cdot 10^{23}}\\& = \frac{6}{5} \cdot 1000000000000000000000 \cdot \frac{1}{\left(6 + \frac{2}{100}\right) \cdot 10^{23}}\\& = \frac{6}{5} \cdot 1000000000000000000000 \cdot \frac{1}{\left(6 + \frac{1}{50}\right) \cdot 10^{23}}\\& = \frac{6}{5} \cdot 1000000000000000000000 \cdot \frac{1}{\frac{301}{50} \cdot 10^{23}}\\& = \frac{6}{5} \cdot 1000000000000000000000 \cdot \frac{1}{\frac{301}{50} \cdot 100000000000000000000000}\\& = \frac{6}{5} \cdot \frac{1000000000000000000000}{602000000000000000000000}\\& = \frac{6}{5} \cdot \frac{1}{602}\\& = \frac{3}{1505}\end{aligned}\]

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