1.4*10^9 upon3.475*10^6

asked by guest
on Dec 28, 2024 at 7:49 am



You asked:

Evaluate the expression: \(\frac{1.4 \cdot {10}^{9}}{3.475 \cdot {10}^{6}}\)

MathBot Answer:

\[\frac{1.4 \cdot {10}^{9}}{3.475 \cdot {10}^{6}} = \frac{56000}{139} = 402.\overline{8776978417266187050359712230215827338129496402}\]

\[\begin{aligned}\frac{1.4 \cdot {10}^{9}}{3.475 \cdot {10}^{6}}& = \left(1 + \frac{4}{10}\right) \cdot 10^{9} \cdot \frac{1}{\left(3 + \frac{475}{1000}\right) \cdot 10^{6}}\\& = \left(1 + \frac{2}{5}\right) \cdot 10^{9} \cdot \frac{1}{\left(3 + \frac{475}{1000}\right) \cdot 10^{6}}\\& = \frac{7}{5} \cdot 10^{9} \cdot \frac{1}{\left(3 + \frac{475}{1000}\right) \cdot 10^{6}}\\& = \frac{7}{5} \cdot 1000000000 \cdot \frac{1}{\left(3 + \frac{475}{1000}\right) \cdot 10^{6}}\\& = \frac{7}{5} \cdot 1000000000 \cdot \frac{1}{\left(3 + \frac{19}{40}\right) \cdot 10^{6}}\\& = \frac{7}{5} \cdot 1000000000 \cdot \frac{1}{\frac{139}{40} \cdot 10^{6}}\\& = \frac{7}{5} \cdot 1000000000 \cdot \frac{1}{\frac{139}{40} \cdot 1000000}\\& = \frac{7}{5} \cdot \frac{1000000000}{3475000}\\& = \frac{7}{5} \cdot \frac{40000}{139}\\& = \frac{56000}{139}\end{aligned}\]

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