(8 * 10^-5) + (6 * 10^-5) / 5.6 * 10^3

asked by guest
on Oct 21, 2024 at 4:07 pm



You asked:

Evaluate the expression: \(8 \cdot {10}^{-5} + \frac{6 \cdot {10}^{-5}}{5.6} \cdot {10}^{3}\)

MathBot Answer:

\[8 \cdot {10}^{-5} + \frac{6 \cdot {10}^{-5}}{5.6} \cdot {10}^{3} = \frac{1889}{175000} = 0.01079\overline{428571}\]

\[\begin{aligned}8 \cdot {10}^{-5} + \frac{6 \cdot {10}^{-5}}{5.6} \cdot {10}^{3}& = 8 \cdot \frac{1}{10^{5}} + 6 \cdot \frac{1}{10^{5}} \cdot \frac{1}{5 + \frac{6}{10}} \cdot 10^{3}\\& = \frac{8}{100000} + 6 \cdot \frac{1}{10^{5}} \cdot \frac{1}{5 + \frac{6}{10}} \cdot 10^{3}\\& = \frac{1}{12500} + 6 \cdot \frac{1}{10^{5}} \cdot \frac{1}{5 + \frac{6}{10}} \cdot 10^{3}\\& = \frac{1}{12500} + \frac{6}{100000} \cdot \frac{1}{5 + \frac{6}{10}} \cdot 10^{3}\\& = \frac{1}{12500} + \frac{6}{100000} \cdot \frac{1}{5 + \frac{3}{5}} \cdot 10^{3}\\& = \frac{1}{12500} + \frac{6}{100000} \cdot \frac{1}{\frac{28}{5}} \cdot 10^{3}\\& = \frac{1}{12500} + \frac{6}{100000} \cdot \frac{5}{28} \cdot 10^{3}\\& = \frac{1}{12500} + \frac{6}{100000} \cdot \frac{5}{28} \cdot 1000\\& = \frac{1}{12500} + \frac{3}{50000} \cdot \frac{5}{28} \cdot 1000\\& = \frac{1}{12500} + \frac{3}{280000} \cdot 1000\\& = \frac{1}{12500} + \frac{3}{280}\\& = \frac{1889}{175000}\end{aligned}\]

+ Submit Question