3.01 x $10^{7}$ / 2.2 x $10^{9}$

asked by guest
on Dec 27, 2024 at 4:50 am



You asked:

Evaluate the expression: \(\frac{3.01 \cdot {10}^{7}}{2.2} \cdot {10}^{9}\)

MathBot Answer:

\[\frac{3.01 \cdot {10}^{7}}{2.2} \cdot {10}^{9} = \frac{150500000000000000}{11} = 13681818181818181.\overline{81}\]

\[\begin{aligned}\frac{3.01 \cdot {10}^{7}}{2.2} \cdot {10}^{9}& = \left(3 + \frac{1}{100}\right) \cdot 10^{7} \cdot \frac{1}{2 + \frac{2}{10}} \cdot 10^{9}\\& = \frac{301}{100} \cdot 10^{7} \cdot \frac{1}{2 + \frac{2}{10}} \cdot 10^{9}\\& = \frac{301}{100} \cdot 10000000 \cdot \frac{1}{2 + \frac{2}{10}} \cdot 10^{9}\\& = \frac{301}{100} \cdot 10000000 \cdot \frac{1}{2 + \frac{1}{5}} \cdot 10^{9}\\& = \frac{301}{100} \cdot 10000000 \cdot \frac{1}{\frac{11}{5}} \cdot 10^{9}\\& = \frac{301}{100} \cdot 10000000 \cdot \frac{5}{11} \cdot 10^{9}\\& = \frac{301}{100} \cdot 10000000 \cdot \frac{5}{11} \cdot 1000000000\\& = 30100000 \cdot \frac{5}{11} \cdot 1000000000\\& = \frac{150500000}{11} \cdot 1000000000\\& = \frac{150500000000000000}{11}\end{aligned}\]

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