6.67*10^-17/6.4^2

asked by guest
on Jan 26, 2025 at 8:25 pm



You asked:

Evaluate the expression: \(\frac{6.67 \cdot {10}^{-17}}{{6.4}^{2}}\)

MathBot Answer:

\[\frac{6.67 \cdot {10}^{-17}}{{6.4}^{2}} = \frac{667}{409600000000000000000} = 0.00000000000000000162841796875\]

\[\begin{aligned}\frac{6.67 \cdot {10}^{-17}}{{6.4}^{2}}& = \left(6 + \frac{67}{100}\right) \cdot \frac{1}{10^{17}} \cdot \frac{1}{\left(6 + \frac{4}{10}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{1}{10^{17}} \cdot \frac{1}{\left(6 + \frac{4}{10}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{1}{100000000000000000} \cdot \frac{1}{\left(6 + \frac{4}{10}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{1}{100000000000000000} \cdot \frac{1}{\left(6 + \frac{2}{5}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{1}{100000000000000000} \cdot \frac{1}{\left(\frac{32}{5}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{1}{100000000000000000} \cdot \frac{1}{\frac{1024}{25}}\\& = \frac{667}{100} \cdot \frac{1}{4096000000000000000}\\& = \frac{667}{409600000000000000000}\end{aligned}\]

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