3.8*10^-8 / 5.6 * 10^6

asked by guest
on Nov 24, 2024 at 3:00 am



You asked:

Evaluate the expression: \(\frac{3.8 \cdot {10}^{-8}}{5.6} \cdot {10}^{6}\)

MathBot Answer:

\[\frac{3.8 \cdot {10}^{-8}}{5.6} \cdot {10}^{6} = \frac{19}{2800} = 0.0067\overline{857142}\]

\[\begin{aligned}\frac{3.8 \cdot {10}^{-8}}{5.6} \cdot {10}^{6}& = \left(3 + \frac{8}{10}\right) \cdot \frac{1}{10^{8}} \cdot \frac{1}{5 + \frac{6}{10}} \cdot 10^{6}\\& = \left(3 + \frac{4}{5}\right) \cdot \frac{1}{10^{8}} \cdot \frac{1}{5 + \frac{6}{10}} \cdot 10^{6}\\& = \frac{19}{5} \cdot \frac{1}{10^{8}} \cdot \frac{1}{5 + \frac{6}{10}} \cdot 10^{6}\\& = \frac{19}{5} \cdot \frac{1}{100000000} \cdot \frac{1}{5 + \frac{6}{10}} \cdot 10^{6}\\& = \frac{19}{5} \cdot \frac{1}{100000000} \cdot \frac{1}{5 + \frac{3}{5}} \cdot 10^{6}\\& = \frac{19}{5} \cdot \frac{1}{100000000} \cdot \frac{1}{\frac{28}{5}} \cdot 10^{6}\\& = \frac{19}{5} \cdot \frac{1}{100000000} \cdot \frac{5}{28} \cdot 10^{6}\\& = \frac{19}{5} \cdot \frac{1}{100000000} \cdot \frac{5}{28} \cdot 1000000\\& = \frac{19}{500000000} \cdot \frac{5}{28} \cdot 1000000\\& = \frac{19}{2800000000} \cdot 1000000\\& = \frac{19}{2800}\end{aligned}\]

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