Convert gravet-force to atomic unit of force

Learn how to convert 1 gravet-force to atomic unit of force step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(gravet-force\right)={\color{rgb(20,165,174)} x}\left(atomic \text{ } unit \text{ } of \text{ } force\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(newton\right)\)
\(\text{Left side: 1.0 } \left(gravet-force\right) = {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}\left(newton\right)} = {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}\left(N\right)}\)
\(\text{Right side: 1.0 } \left(atomic \text{ } unit \text{ } of \text{ } force\right) = {\color{rgb(125,164,120)} 8.23872206 \times 10^{-8}\left(newton\right)} = {\color{rgb(125,164,120)} 8.23872206 \times 10^{-8}\left(N\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(gravet-force\right)={\color{rgb(20,165,174)} x}\left(atomic \text{ } unit \text{ } of \text{ } force\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}} \times {\color{rgb(89,182,91)} \left(newton\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 8.23872206 \times 10^{-8}}} \times {\color{rgb(125,164,120)} \left(newton\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(N\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 8.23872206 \times 10^{-8}} \cdot {\color{rgb(125,164,120)} \left(N\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(N\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 8.23872206 \times 10^{-8}} \times {\color{rgb(125,164,120)} \cancel{\left(N\right)}}\)
\(\text{Conversion Equation}\)
\(9.80665 \times 10^{-3} = {\color{rgb(20,165,174)} x} \times 8.23872206 \times 10^{-8}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(9.80665 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}} = {\color{rgb(20,165,174)} x} \times 8.23872206 \times {\color{rgb(255,204,153)} \cancelto{10^{-5}}{10^{-8}}}\)
\(\text{Simplify}\)
\(9.80665 = {\color{rgb(20,165,174)} x} \times 8.23872206 \times 10^{-5}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 8.23872206 \times 10^{-5} = 9.80665\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{8.23872206 \times 10^{-5}}\right)\)
\({\color{rgb(20,165,174)} x} \times 8.23872206 \times 10^{-5} \times \dfrac{1.0}{8.23872206 \times 10^{-5}} = 9.80665 \times \dfrac{1.0}{8.23872206 \times 10^{-5}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{8.23872206}} \times {\color{rgb(99,194,222)} \cancel{10^{-5}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{8.23872206}} \times {\color{rgb(99,194,222)} \cancel{10^{-5}}}} = 9.80665 \times \dfrac{1.0}{8.23872206 \times 10^{-5}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{9.80665}{8.23872206 \times 10^{-5}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-5}}\text{ can be rewritten to }10^{5}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{5} \times 9.80665}{8.23872206}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx119031.20324\approx1.1903 \times 10^{5}\)
\(\text{Conversion Equation}\)
\(1.0\left(gravet-force\right)\approx{\color{rgb(20,165,174)} 1.1903 \times 10^{5}}\left(atomic \text{ } unit \text{ } of \text{ } force\right)\)

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