10^-4/1.984*10^-19

asked by guest
on Jan 18, 2025 at 2:54 am



You asked:

Evaluate the expression: \(\frac{{10}^{-4}}{1.984} \cdot {10}^{-19}\)

MathBot Answer:

\[\frac{{10}^{-4}}{1.984} \cdot {10}^{-19} = \frac{1}{198400000000000000000000} = 0.00000000000000000000000504\overline{032258064516129}\]

\[\begin{aligned}\frac{{10}^{-4}}{1.984} \cdot {10}^{-19}& = \frac{1}{10^{4}} \cdot \frac{1}{1 + \frac{984}{1000}} \cdot \frac{1}{10^{19}}\\& = \frac{1}{10000} \cdot \frac{1}{1 + \frac{984}{1000}} \cdot \frac{1}{10^{19}}\\& = \frac{1}{10000} \cdot \frac{1}{1 + \frac{123}{125}} \cdot \frac{1}{10^{19}}\\& = \frac{1}{10000} \cdot \frac{1}{\frac{248}{125}} \cdot \frac{1}{10^{19}}\\& = \frac{1}{10000} \cdot \frac{125}{248} \cdot \frac{1}{10^{19}}\\& = \frac{1}{10000} \cdot \frac{125}{248} \cdot \frac{1}{10000000000000000000}\\& = \frac{1}{19840} \cdot \frac{1}{10000000000000000000}\\& = \frac{1}{198400000000000000000000}\end{aligned}\]

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